On Friday I posted this puzzle… imagine that you accept a new job and are offered one of two possible pay schemes.

Scheme 1) You get a starting salary of $100 per year, and then a $20 pay rise each year.

Scheme 2) You get a starting salary of $100 per year, and then a $5 pay rise every six months.

In either case, you are paid every 6 months. Which scheme is better?

If you have not tried to solve it, have a go now. For everyone else the answer is after the break.

Intuitively Scheme 1 sounds better. However, when you take a look at the maths a different picture emerges…

In Scheme 1…

In the first year you get $50 + $50 = $100

And in the second year you get $60 + $60 = $120

In Scheme 2….

In the first year you get $50 + $55 = $105

And in the second year you get $60 + $65 = $125

So Scheme 2 will always be better than Scheme 1.

Did you solve it? Any other answers?

Oh, and if you enjoy the Friday Puzzle, remember that I have produced a kindle ebook containing 101 of the previous Friday Puzzles! It is called **PUZZLED** and is available in the UK here and USA here.

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Scheme 2, and I didn’t even do any math. I likened it to the math question like this that you can either get paid a set amount of money every day for a month or get a pay starting at $0.01 and it doubles every day (.01 on the first day then .02 on the second day and so on) after that for the month. It’s been a long while since I did that puzzle, but I remember the increments being a better pay out in the end.

Yes its really simple maths that you can do in you head (excel, pah!). But I do wonder how many people who said on friday that the answer was obvious, or that there was no real puzzle, were, in fact, wrong!

I agree totally, in two 6 monthly installments.

Oh dear Richard, you appear to have made the same mistake as Marilyn vos Savant (see here: http://www.donaldsauter.com/brain-teasers.htm#raise)

It s a pay rise, not a bonus. So scheme two involves a pay rise of $5 – i.e. pay after 6 months is $105 PER YEAR, which is $52.50 for the second six month period. The sums looks like this:

In Scheme 1…

In the first year you get $50 + $50 = $100

And in the second year you get $60 + $60 = $120

In Scheme 2….

In the first year you get $50 + $52.50 = $102.50

And in the second year you get $55 + $57.50 = $112.50

So Scheme 2 will always be better than Scheme 1 in the first year, but Scheme 1 catches up after year two and always stays ahead after that.

Oh dear you seem to think that pointing out that the vague grammar of the question may allow for another solution makes everyone but you wrong. The question is clear that the first raise is $20 per year and the second raise is $5 per 6 months.

@Tort, it’s not a case of vague grammar allowing another solution. The term “pay rise” is used in different ways in both schemes. If it is used consistently, then scheme 1 will always be better, whether “pay rise” means per year or per paycheck.

Yes, this!

I agree with @Ned and @Emlyn. The wording of the problem states $5 ‘pay rise’ which I took to mean that the pay would then be $105 p.a. or $52.50 per six months.

Surely the problem should have read $10 pay rise every six months vs. $20 pay rise every year…

Exactly. The wording implies that you get a $5 payrise over the year, which would be 2.50 over the 6 months. I knew Richard must have meant it was a 5$/6 months = 10$/year, otherwise there would be no puzzle – it resulted in a long argument over a google spreadsheet with a friend in copenhagen that lasted all weekend.

Very good point.

If the $5 raise is added directly to the 6mo pay-out, it means a $10 yearly raise every 6 months.

Great puzzle, especially since Inever thought about the logic of yearly salaries. The catch mentioned is even more curious.

Thanks!

Of course this is the right answer… Richard is comparing apples with oranges.

This. I worked it out both ways, because the wording was so ambiguous.

I had Ned’s solution.

It is a pay rise of the salary. So starting with $100, and adding $20, means your new salary now is $120. Starting with $100, and adding $5 twice means your salary is $110 after a year.

Since the first addition of $5 was before the second payment of the (half) salary, you get (half of $105) $52.50. Ending up at $102.50 after year 1.

Like Berber Anna I worked it out both ways and my opinion is that the original question is phrased ambiguously on purpose in order to deceive. So I got the answer but I didn’t like it.

Mike.

I also agree with Ned.

I disagree that the question was ambiguous however. The way the question is written it is very clear that #1 is the best choice. The only way to get the answer that Richard gives is if you interpret the question incorrectly.

If he is going to take “a $5 pay rise every six months” to mean that every 6 months his paycheck is $5 more, then the only way to interpret “a $20 pay rise each year” is that every year his paycheck is $20 more.

Though in fairness, we all knew what the intention of the puzzle was even if it was worded incorrectly.

Count me as another who agrees with Ned. The wording is confusing, but not really ambiguous. If you have a salary of $100 a year, and you get a 5$ pay raise every six months, it’s still a raise in your yearly salary, so you only see half that in six months. Richard is wrong. Not poorly worded, but fooled by the puzzle himself and wrong.

Not a native english speaker I conclude that scheme 1 is better:

First three years of scheme 1: 50+50 | 60+60 | 70+70 = 340

First three years of scheme 2: 50+50 | 55+60 | 65+70 = 320

The issue is the wording: “You get a starting salary of $100 per year, and THEN a $20 pay rise each year.” which means to me that after the first year you get the first raise. Which would also be the realistic scenario – at least in Austria, where you’d normally get the intro salary for 12 months and the first contractual raise a year afterwards.

That is the same assumption I made, so I got it wrong this week and I am an English speaker!

Yes! Even in scheme 2 there will be the first rise after one year!

So both salaries start with 100 in the first year!

@Ned — for Scheme 2 the problem states “a $5 pay rise every six months,” not “a $5 annual raise given after the first six months.” It seems very clear and precise to me.

I don’t think so. The term “pay rise” means an increase in your quoted salary. The fact that it happens to be given every 6 months does not change that. If it was given every two years would you argue that it should only be $2.50 per year? What if it is a one-off pay rise?

Henry, if you were offered a job paying £30k / year, paid monthly, and told that in 6 months you’d get a rise of £6k you would take that as meaning that your annual salary is £36k / year. Your first 6 pay packets would be £30k / 12 = £2.5k and the 7th one onwards would be £36k / 12 = £3k.

You wouldn’t expect each individual pay packet to increase by £6k, to £8·5k / month.

Nor would you interpret the raise after 6 months as being an amount per 6-months; you wouldn’t claim that your monthly pay is (£30k / 12) + (£6k / 6) = £3·5k.

Getting paid every 6 months rather than every 1 month doesn’t magically change the meaning of ‘pay rise’ from being per year to being per payment frequency or per raise frequency.

So the quoted pay rise of $5 should be a rise in the annual rate, of which only $5 / 2 $2·50 is added to each pay packet.

that’s exactly what i got, this one very interesting but a little too easy.

Why does the $20 payrise not get added on at the 1 year point, but only afterwards at 18 months, but the $5 rise gets added on at the 6 month point? You are dealing with the payrises inconsistently!

Wait, nevermind, got that wrong!

You have definitely used “pay rise” in two different ways in the two different schemes. In both schemes you define the base salary of $100 in terms of one year, yet in your answer in one of the schemes a $5 pay rise actually means a $10 increase in pay over a year, while the $20 pay rise only gets you $20 a year extra. The counterintuitive result is actually a case of poor definition in the problem statement.

You’re new here, aren’t you? 😛

Get used to tricky wording in Richard’s puzzles.

@Mchl the problem is, that usually when you read the tricky wording carefully it actually makes sense, that’s part of what makes it a puzzle. In this case it is just wrong.

I think this anwer is wrong too.

After 6 months you’ve had a $5 payrise, so your annual pay (since your salary is quoted by year) is now $105. Which means your second pay cheque is 52.5.

By the start of the second year you’ve had 2 $5 payrises so your pay is now $110, and you so get $55 etc

So clearly 1 is better.

Why does the “pay rise” in first case apply to the yearly salary and in second case to the 6-month pay?

How about this for alternate wording: First scenario: you get $100 annual salary and a $20 increase in annual salary every year. Second scenario: you get $100 annual salary and a $10 increase to annual salary every 6 months. And just like that, with clear wording, the puzzle disappears.

Puzzles where the only “puzzle” is trying to figure out what the hell the author has tried to say are dumb.

It could be better worded. The $5 pay rise should say its per pay period. Since all the other pay figures are annual one might reasonably assume the $5 pay rise meant annually.

I agree, especially since the term “pay rise” is already used once to mean annually, then we are supposed to guess that it has silently been redefined.

Ha! I did get it right!

@Henry – Sorry, but I agree with Ned.

On scheme 2, your salary begins at £100 p.a.

After 6 months, you get paid half your salary (£50), and you get a raise of £5.

Your salary is therefore now £105 p.a.

At 12 months, you again get paid half your annual salary…..£52.50, and another raise of £5. brining you to £110

So after 12 months, on scheme 1 your annual salary is now £120, while on scheme 2 it is just £110.

The error Richard makes I think is in applying the pay rise to the pro-rata’d (paid) salary rather than the BASE salary. The clue is in the explanation that reads “And in the second year you get $60 + $65 = $125” – you don’t. At THAT point your salary is £100 +£5 +£5 (start salary plus two £5 increments) for a salary of £110 paid 6 monthly.

This reminds me of the old “£10 each for a kettle ….where did the £1 go?” puzzle!

I’m with Stu and Ed on this one. The pay rise is to an annual salary. If you get a pa yrise at work (and you are salaried) it gets pro-rated over the months.

I meant Ned!

Interpretation 1 (when pay rise means that your yearly salary will rise)

Scheme 1:

year 1: 50$ 50$

year 2: 60$ 60$

year 3: 70$ 70$ etc.

Scheme 2:

year 1: 50$ 55$ – not 52.5$ because that wouldn’t make the yearly salary 105$ just 102.5$

year 2: 55$ (110/2) 60$ – becasue 55$ + the second term salary now have to be 115

year 3: 60$ (120/2) 65$

Interpretation 2 (when pay rise refers to the amount you receive each payment)

scheme 1:

50$ 50$ 70$ 70$!

scheme 2:

50$ 55$ 60$ 65$

Richard got the two mixed up, althought his solution makes sense too. The original one is correct only because otherwise there is no catch. I don’t like this puzzle.

I followed exactly that line of thought. If you stayed in the job for 40 years and had chosen Scheme 2 you ‘d be $7700 worse off!

A pay rise after 6 months doesn’t mean you backdate that payrise to the start of the year, in any country. This means that scheme 1 is better. Unfortunately the puzzle was a bit too clever for itself.

I have to agree with others that, given the generally accepted way in which pay rises work, scheme 1 is the better option. At best, the question is worded badly; at worst, the “official” answer is wrong. 🙂

If you search the web you’ll find that this puzzle has been widely discussed, like the famed ‘Monty Hall / 3 Doors’ puzzle, and it seems to generate an almost equal amount of controversy.

The controversy in this cases arises because the wording is ambiguous. Does a ‘$5 pay rise every six months’ mean that in the second half of Year 1 you get paid 105 or 102.50? Different people insist on different interpretations, which gives rise to the controversy. Of course, both sides can offer strong reasons as to why their own view is the right one.

The more tenable but rather dull position is to say that we can only arrive at a definitive answer if the wording is clarified.

When Richard posted this on Friday, he said it was one of his favourite puzzles. I suspect that maybe this is because he’s perfectly well aware of the subtle ambiguity it contains and the fact that it can give rise to such controversy and dispute.

I don’t see a problem with the solution, scheme 1 gets an extra 20 every year, scheme 2 gets 5 every six months, just add them up over a few years.

I found it interesting that the cumulative ammounts even out mid-year then scheme 2 pulls ahead at the end of each year, quite a strange pattern.

Surely the “solution” is based around interpreting the same words in two ways in each case. In 1 your pay rise goes on your salary, in 2 your pay rise goes on your wage.

Alright then. Same words, different behaviour. So why not:

Scheme 1: 50+50=100, 70+70=140, 90+90=180

Scheme 2: 50+52.5=102.5, 55+57.5=112.5, 60+62.5=122.5

Exactly the same behaviour, just swapping it round. Monday puzzle: please, genuinely, tell me what I did here that Richard didn’t, because otherwise I just cannot “get” his solution.

But the wording is ambigous. “Pay raise” is defined differently in each of the options. If in the second option the pay is 50, 55, 60, 65 ect. then the pay in the second option should be 50, 50, 70, 70, 90…

The fact that the second option comes out ahead in Richards interpretaion is simply because the annual pay raise is the same in both options, but you get a better pay once every year.

It all depends when the salary increases kick in.

Richard interprets the problem as the 6 monthly increase kicking in after only six months (first salary increase at the one year pay point), whereas the annual increase only kicks in after two years.

Like many here, I find that somewhat odd.

If both salary increases kick in after the completion of a full year’s service, and the salary for A increases by $20 per year, while B increases by £5 every six months, then the salaries for A and B are as follows (per annum):

1 – $100, $100

2 – $120, $115

3 – $140, $135

4 – $160, $155

5 – $180, $175

So at the end of each year, B’s salary is always $5 behind A.

If, however, the increases kick in after the first payment period, then there are two scenarios regarding A: either their increases occur on the anniversary of their appointment (so A’s first increase is after 1.5 years of service), or on the six month anniversary (A’s first increase is after 1 year of service).

In the first case:

1 – $100, $105

2 – $120, $125

3 – $140, $145

4 – $160, $165

5 – $180, $185

So B’s salary is always $5 ahead of A.

In the second case:

1 – $110, $105

2 – $130, $125

3 – $150, $145

4 – $170, $165

5 – $190, $185

So B’s salary is always $5 behind A.

The wonders of leaving questions open to interpretation 🙂

This is fascinating.

I’ll be eating my words on this not being a Puzzle. However, I need someone to explain to me HOW this can be. I see the numbers, but it doesn’t help. I need to see the *equation* that demonstrates why this occurs (links are fine). Coz my brain refuses to understand how a $20 per year gain is less than a $10 per year gain, just because you change the payment dates.

So equations. Yes, I’m weird like that. Real World numbers mean nothign to me. I need to see the equation 😉

/Z

The thing is that it is not a $10 per year gain. The way Richard interprets the puzzle, it is a $20 per year gain, done in two increments.

Even with the cumulation of the two fivers (I get that part) my brain just don’t get how it can outpace the twenty.

This reminds me never to negotiate salary w. Richard. 🙂

/Z

I had the same “thinking problem” as MasterZap. But then …

When I get $55 for the second half year, that means I have a yearly salary of 110$.

$60 for the next makes $120/year.

So both scemes are a $20-raise-per-year. But because on “B” half of the raise starts 6 month earlier, “B” is allways a little bit in advance.

Perhaps this clears things out for you:

Option 1

Effective yearly salary / amount paid

100 / 50

110 / 55

120 / 60

130 / 65

140 / 70

Option 2

Effective yearly salary / amount paid

100 / 50

100 / 50

120 / 60

120 / 60

140 / 70

So the thing is that while the $20 increase is split between the two months, the $5 is not. So not only is the $5 cumulative, the $20 is split in half.

In one of my previous posts I complained about the different meaning of “pay raise” between the two options. If it had been consistent, the $20 pay raise outpreforms the $5 pay raise.

Ah, thank you! The key insight is that “$5 on a half year is factually equivalent to $10 on a year”, meaning the two $5 half-years are actually the same as the $20 per year. The rest is just lag.

Groovy.

/Z

I should add a couple of things to my last post. First a few corrections. I swapped option 1 and 2. “two months” should be two paydays. And finally list with where the $20 option has the same meaning of “pay raise” as Richard has in his $5 option.

Effective yearly salary / amount paid

100 / 50

100 / 50

140 / 70

140 / 70

160 / 90

160 / 90

I too got Answer 1 as the solution as it states £100 starting salary per year therefore I would not have expected any increase to show up until the third pay date at which point the first scenario would be ahead.

This. Exactly this. “You get a starting salary of $100 per year” means you get paid $100 for the whole of year one, and only in year two does your increment kick in.

Pretty poor advert for his puzzle book.

Especially when this is one of his favorites…

I’m sorry, but i don’t accept as the answer to a puzzle “Words get to mean whatever i want them to mean”

It’s interesting that if you graph the problem, with x being 6 months we get

$20 option

f(x)=20/2X+100

$5 option:

g(x)=5*2X+100

The graph follows the same line, but since the $5 option is paid every 6 months, putting it into columns we can see how the $5 option is $5 up on the other one every other payment

I got Richard’s solution.

The answer is just wrong.

Plan B gets us:

50

52.50

55.00

57.5

60

62.5

65

67.5

There’s nothing in the wording about having your raise go up $5 PER 1/2 YEAR.

This isn’t being pedantic. It changes everything.

It says you get ‘a $5 pay rise every six months’…. how is that not the same?

Well, one shouldn’t expect him to get his sums right: he’s only a psychologist, after all. 😉

The way the question is written the solution can be interpreted in two ways, both of which says option 1 is best

pay rise means: annual salary increase

option 1 / option 2

50 / 50

50 / 52.5

60 / 55

60 / 57.5

70 / 60

…

pay rise means: increase per paycheck

option 1 / option 2

50 / 50

50 / 55

70 / 60

70 / 65

90 / 70

…

If you are going to use the exact same wording to mean 2 different things, then we can just as easily done the following:

option 1 / option 2

50 / 50

50 / 52.5

70 / 55

70 / 57.5

90 / 60

Not only is the solution interpreting the same wording in two different ways, it’s doing it in the only possible way that gives the wrong answer.

I will take my $20 annual raise and sue the company when I find out they don’t understand math.

This!

Did I solve it?… yep! Not sure, why so many objections.

Maybe because the official answer is wrong? 😉

im rubbish at maths and this seems to prove it! i said scheme 1 because

in scheme 1- x=y(100)+(y-1)X20 x= total money

and in scheme 2- x=y(100)+(y-1)X10 y= number of years

but even now you’ve given the solution i still can’t see where i’ve gone wrong!

This is hilarious. All these people up in arms because instead of reading exactly what’s written, they want to add interpretations of terms, even if that directly contradicts the plain exact wording.

I missed the puzzle on Friday, but a plain reading of exactly the words written gives you richard’s solution, like it or not.

Please explain how a pay raise can be defined differently then.

please do explain. Why is it ok to interpret the same wording in two different ways?

Richard used “pay rise” differently in the two examples.

Both groups get paid every 6 mos.

If you want to say salary jumps by $5 and not $2.50 for the second group, then you have to say that the salary jumps by $20 and not $10 for the first group.

The answer is unequivocally wrong no matter how you define “pay rise”.

I hate to be pedantic (especially in this forum!) but the question WAS ambiguous … it depends entirely on how long you stay in job for … if you leave after 11 months, clearly Scheme 2 is better ….

i got it 😀

Since almost every puzzle Richard posts is ambiguous, incomplete or plain incorrect, I don’t see this as a ringing endorsement for his new puzzle book – although maybe the edition without the answers would be a good resource for a critical-thinking course.

To those who claim the wording is wrong, ie =pay rise=5 for the full year ie first half you make 100 a year (50) and second half 105 a year(52.50) I do see your point, but it wouldnt really be a good puzzle then. the fun thing about it(even if the wording was unclear) is that the 2 options actually rises the same, which is unintuitive in itself, and on top of that, the $5 option is one step ahead. So hers a suggestion: Take a pill, breathe and relax, and pretend that the wording was more precise, it then becomes kind of mind-bending, intuitively one would think, even with Richards assumptions, that the two fivers would add up to 10 and so on, thats the fun part. Stop being so annoyingly pendantic. Even if you are right.

It’s not a matter of pedantry. The only way a puzzle of this type could be ‘interesting’ is if it was actually consistent in its definitions. There is a way to do it by carefully choosing the figures and having two different pay progressions: however, Richard’s puzzle here has not chosen such careful figures!

Either “pay rise” means “an increase to your annual salary” or it means “an increase in take home pay at your next pay date”. You can’t have it mean something different for each option. That’s not a puzzle. Nor it is “surprising” or “interesting”: it’s just nonsense.

I agree with Anders. I interpreted the wording just as Richard has in his solution, and was fascinated by the result, which was not at all what I was expecting.

Those people complaining about the interpretation seem to be missing the beauty of the answer by going out of their way to find it ambiguous. Maybe you’re right, but isn’t the answer (with the wording clarified, if you must) fascinating?

@Jeremy

With the wording clarified it says: Would you prefer a $10 raise twice a year or a $20 raise once a year? Facinating

What? This article uses two different ways of raising pay – are we tlaking about a rise on each pay, or a rise on theyerly amount? Without that ambiguity, the problem goes away.

Maybe I’m missing something, but I had Richard’s solution and I still can’t see what’s wrong with it.

If my boss told me I’d be getting ‘a $5 pay rise every six months’, I’d expect my annual salary to increase by $5 six months from now, and then by another $5 six months after that, and so on. If they only paid me an extra $2.50 the first time, I’d be looking for another job.

Perhaps the answer lies in davee’s statement above: Either “pay rise” means “an increase to your annual salary” or it means “an increase in take home pay at your next pay date”.

I think it means ‘Your annual salary will increase to that level AT THAT POINT, ie half way through the year’, which is a third option.

It’s perfectly possible to have your annual salary raised at any point in the cycle without that salary having to be applied over the entire calendar year, isn’t it?

You can’t do it that way, though.

If you increase take-home pay by $5 after six months in Scheme 2, from $50 to $55 (“$5 pay rise every six months”), then the same logic says that after one year in Scheme 1 your pay should increase from $50 to $70(“$20 pay rise each year”). And Scheme 1 ‘wins’.

Logic means that either both of the above increases are made as described, or neither, since the description used in the question is the same.

If, on the other hand, you assume that “pay rise” relates to annual pay on a pro-rata basis, then you get $50, $50, $60, $60 for Scheme 1 and $50, $52.50, $55, $57.50 for Scheme 2. Here Scheme 1 also ‘wins’.

Mixing and matching the meaning of the descriptions cannot be done in any meaningful way.

The puzzle is poorly written, in my opinion. Or “wrong”, if you prefer 😉

‘then the same logic says that after one year in Scheme 1 your pay should increase from $50 to $70(“$20 pay rise each year”).’

Yes, but since you get paid every six months, you get the extra $20 in two instalments. You’re being paid in arrears, every six months, at the prevailing rate. That is surely how real salaries work, no?

“That is surely how real salaries work, no?”

If you are insisting on approaching this in the manner of how “real salaries work”, then there’s no way that you can simultaneously justify getting $55 in the second period of Scheme 2.

If you start with a salary of $100 PER YEAR, and this goes up to $105 PER YEAR after six months, you will next get paid six months worth of $105, that is $52.50. (If you get a pay rise during the year, it is never normally backdated to the start of the year. )

As you said yourself, that’s how real salaries work.

Oh please, I can’t believe the bitching and moaning. At least I owned up to missing the puzzle, and I think everyone whining are afraid to admit they miss the puzzle.

There is a clear interpretation of “pay rise”, as a rise in pay over the period the pay was defined in. In one case, the pay was defined per-year, in the other case, pay was defined per six months. Simple, really. If Richard hadn’t said “either way, you get payed ever six months” it would have been clearer – but I don’t see how that changes anything.

Come on, admit it, like me, you are so brain-screwed by the actual puzzle, that you are trying to weazel yourself out of having seen it!

/Z

Couldn’t have put it better myself.

I disagree. If you look at the comments from the original Friday post you will see that there are several people, myself included, that pointed out the very poor wording before the “solution” was released on Monday.

Looking back, I think this was a reasonable puzzle. It’s kinda interesting how many people took the same sentence and defined it two different ways under the same context.

this is so amusing… :)))

no wonder why the court all over the world need such a looooooooooooonngg time to solve a problem. toast to mr. Wiseman.

oooww… and to all who post your comment.

Definition of pay rise-“an increase in the amount of money you are paid for doing your job”. Therefore, if your pay gets raised £5 every 6 months, at the end of a year, your pay has been raised £10! I’m with Wiseman!

@Michael: Pay rise is applied to one’s salary, so you’re correct, your salary will be $10 higher at the end of the first year. So, at that point, your salary is $100 plus $10 = $110 – this means your salary for first half of year 2 is $110/2 = $55

I don’t understand why people are failing to understand this.

If I’m earning £12,000 per year – that is, £1,000 per month – and I’m told I “get a £1,000 pay rise”, I *don’t* expect to sudden get £2,000 per month. That’s just daft…

The problem is the language lies, I think, as follows.

If this were a “normal” job, and the person were paid MONTHLY, then nobody – I think – would be arguing that their monthly wage of £8.33 a month would jump to £12.33 a month when they got their £5 pay rise after the first six months – same as nobody would argue that after a year on acheme one their monthly pay would jump from £8.33 to £28.33…

Or maybe they would: but if you argue it that way for ONE scheme, you have to aply it equally to BOTH schemes – and hence if you think that in year two scheme 2 should get £60 and £65, then (by the same logic) scheme 1 should receive £70 and £70 each year – when their six-monthly receives its annual “£20 per pay period” increment.

To make scheme 2 the better scheme, you MUST treat the two identically worded schemes as meaning different things…..in which case why not ALSO assume that under scheme 1, although you were promised to be paid every 6 months, you actually get nothing at the 6 month point…..because your promised salary was £100 per year – and the year is not yet up!

Define the problem. If you were offered either of these as a salary, I suspect you’d clarify it, in order to make a decision?

When I read the question I just shrugged, the same way I shrug at the termsheets for wacky deals across my desk every week. Richard, very good if it was intended, but I suspect brainteasers are not supposed to be ill-defined.

Define problem, solve it – ‘assume’ puts an ass in front of u and me etc…

You could look at it another way in which scheme 1 comes out the victor:

If we assume the pay rise is immediate:

Scheme 1

Year 1: 50 + 60 = 110

Year 2: 60 + 70 = 130

Year 3: 70 + 80 = 150

Scheme 2

Year 1: 52.50 + 55 = 107.50

Year 2: 57.50 + 60 = 117.50

Year 3: 62.50 + 65 = 127.50

As you can see, scheme 1 is the clear winner in this circumstance.

A number of people I discussed it with had exactly the same argument, i.e. that salary increases should be consistently per year. Personally I think it’s clear as it is, but you could reword the puzzle as follows. I think this still keeps the essence of the puzzle (i.e. $20 per year vs $10 per year looks better, but isn’t because of the earlier increase), whilst removing any ambiguity as to how the pay rises are applied:

—-

You’re offered one of two possible pay schemes.

Scheme 1) You get a starting salary of $50 per six months, and then a $20 pay rise per year.

Scheme 2) You get a starting salary of $50 per six months, and a $5 pay rise every six months.

Which scheme is better?

They both suck. You’re only making $100 a year?! Keep job hunting!