On Friday I set this puzzle….

A bottle and a cork together cost $1.10. The bottle costs $1.00 more than the cork. How much does the cork cost?

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

Let’s call the bottle B and the cork C. We know that

B= 1 + C and B+ C=1.10

By substituting B into the 2nd equation, we get:

(1+C) + C= 1.10

so 1 + 2C = 1.10

so 2C=.10

so the cork costs .05

and the bottle costs 1.05

Did you solve it?

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called **PUZZLED** and is available for the**Kindle** (UK here and USA here) and on the **iBookstore** (UK here in the USAhere). You can try 101 of the puzzles for free here.

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got it. 6th grade math. 🙂

Ah ha! I said it was simultaneous equations.

This is way too simple for sim.equations! One costs X the other costs a dollar more or X+1 The two cost $1.10 so X+X+1=$1.10 2X+1=1.10 so 2X=.10 then X=.05 So one costs a nickel the other $1.05

Not sure I would call that a puzzle. I was hoping there was a twist that I missed…

I was also looking for the twist. The obvious answer came too easily. I was thinking along the lines of paying corkage for having a bottle opened or it being devalued once it was opened but the question just wasn’t worded that way. My 4 year old son can divide 10p in half.

show off!

A knife, a fork, a bottle and a cork. That’s the way we spell New York.

…right on…

The twist was the first answer that came in mind may be 1$ if you read too quick. Once you read for a second, the correct solution is obvious.

Try it with your friends. 😉

Well I couldn’t do it and I’m not in 6th grade

but why if

2C=.10

does it mean that

C = 5

Surely that is not a valid step. Perhaps Cs are charged at buy-one, get one free, so one cost .10 and one cost 0.

without more background to the cork and bottle wholesaler’s pricing structure, we can say very little.

C= 0.05, not 5.

yes, thanks chris.

now we hae five possible answers. $.10, 10c, 0.05c, $0.50c and zero.

these puzzles leave too much to the imageination

@ Chris. Yep; that’s what the solution says.

uh dude, we know!

I solved this using common sense, no unnecessary algebra. Do I get double points for not being pedantic?

You may have worked it out in your head almost instantly, but in order to work it out, your brain probably followed a similar process to the algebra, but so quickly you didn’t take notice of the steps en-route.

The main purpose of the algebraic equation is to illustrate the logic for anyone that didn’t ‘get it’.

Exactly. Whether you realised it or not, you used algebra in your head ,its just this is such a simple problem it seems knowable by “common sense” If the numbers were more problematic the same basic algebra would be needed

Got it.

I’ve got a better puzzle: When I saw this on on friday, I fetched pen and paper, did equations and neatly underlined the result, which was correct. My husband just thought for two seconds and pronounced the result, which was correct. Which of us is mathematically talented?

There isn’t enough information to say. You know the general theory of simultaneous equations. Now did your husband know that, and was able to apply it very fast to a simple case? Or did he know a little trick that applies to just this kind of problem? There is a little trick for this one, and it comes up often enough to be memorable. If two things add up to total, and you know the difference between them, then what you have to do is subtract the difference from the total, and halve the remainder, to get the smaller number.

I was hoping my instant answer on Friday was wrong, and I’d be taught a lesson, seems not.

This is an interesting problem, but fpr a different reason than trying to solve it properly. For an explanation of why it is so interesting, check out Daniel Kahnemann’s book (2011) “Thinking, Fast and Slow”, a fascinating book on why so many people, including very clever ones, make so many mistakes in their thinking. (Kahnemann won the Nobel Prize for Economics, but is actually a psychologist). In summary, what is interesting is that so many people, if given only a second to answer this problem, get it wrong, even among highly intelligent populations such as students at top universities, where about 50% will get it wrong if required to do it very quickly. What happens is that when thinking instinctively, ie quickly, is that you grasp at the first number that comes into your head, which is often $0.10.

I found the twist in the puzzle.

Richard is laughing because no one has noticed that he, a proper Englishman, used American currency units in this puzzle.

Doing it in my head:

Total = 1.10

Difference = 1.00

What’s left (0.10) is halved, as it is common to the prices of both items, so Cork = 0.05 (cheaper item)

Bottle = 1.00 + Cork = 1.05

Of course, this is just a re-thinking of the simultaneous equation as set out in the given answer, as the answer shown is the method used for more awkward / complex puzzles, when the answer isn’t as obvious.

Thank you for not being one of the many pretensious people commenting about how basic it is without explaining the thought process.

I will openly admit I thought the answer must have been one dollar for the bottle and ten cents for the cork as the question initially appeared (to me) as one that could be solved with very simple subtraction.

Once again thankyou for taking the time to explain in your ways the solution, and not doing so rudely. It’s nice to see there are people out there that realise not everyone thinks the same way as them.

No you are not doing it in your head because right now your typing it on your computer!

Yep. Nice to have an easy one sometimes. 😀

2E(Y+1)= too easy

I think I came across something very similar in one of the Professor Leyton Puzzle games for the Nintendo DS but yeah, got it in a couple of seconds just working out the right combination in my head.

I suppose given the simplicity of the answer on this one I shouldn’t be so excited to have finally gotten one of these right (not that I’ve been trying for long)

The mental arithmetic is a bit easier if you write the equations, on paper or in your head:

b + c = 110

b – c = 100

add, 2b = 210, b = 105, c 5.

i.e., adding the equations is simpler than the “substitution” method when one variable dros out.

Less than a second, but I thought there must be a catch and re-read the problem.

Reminds me of the puzzle: I have in my pocket, 2 coins totalling 25 cents. One is not a 5-cent coin. What are the coins?

If that was pence rather than cents, then I would say to you, just to annoy you, two half-crowns. Though sadly the half-crown, worth 12.5p in the decimal currency, ceased to be legal tender at the moment that Britain adopted decimal currency. Though old sixpences, worth 2.5p after decimalisation, continued to be legal tender for 10 more years. It is notable that Portugal also had a 2.5 Escudo coin that continued to be legal tender up until the time they adopted the Euro, even though they had taken 1, 2 and 0.5 out of circulation.

I posed this old psychology question to my 8-year-old at the dinner table a few weeks ago and he got it right in about 1 second. Maybe you have to be an adult to think it is hard.

Read Nobel laureate Kahneman’s book, “Thinking Fast and Slow” for the explanation of this “puzzle.” It is fascinating.

Knew it wasn’t £1 and 10p but didn’t have time to investigate further, think I would have got there eventually

It is not a puzzle,but a normal math stuff.haha

Hello, just wanted to mention, I loved this post. It

was helpful. Keep on posting!

Foodstuff really should be positioned with a good deal of ease and shouldn’t look cluttered.

The cabinet body materials commonly used wood, metal, paint plates, egger etc.

Ensure you will find stunning flowers on the table.

I dissagree with the answer given. In common life the cork could very well cost 10 cents and the bottle 1.00. If you paid me 10 cents and i then said you could have the bottle too for a dollar more, the you would have paid 1.10 for both and the bottle would still be a dollar more than the cork. In the algebraic expression it states that “we know that B= 1+C” but in reality we dont have to “know” that B has no other option but to exist as a combination of (1+C)..thats just a possible way. B could very well exist simply as 1. Its much simpler to use common sense than to turn it into algebra.

Never mind..I saw my error..I was thinking a dollar more as in “for an additional dollar” not keeping the dollar difference.

I’m right there with ya.. My wife and I are nurses.. And our answer makes the most practical and logical sense.. Lol

Why are there 2 corks now?

(1+C)+C?

Total = $26.

Solution:

The cost of an apple is $1

Since it is mentioned that the orange is $9 more than the apple.

Cost of orange = $10;

Also watermelon costed $5 more than the Orange.

So cost of watermelon = $15

So if I buy all 3 the total I have to pay is;

1 + 10 + 15 = $26

Source from web:- http://puzzle.queryhome.com/16344/apple-costs-orange-costs-apple-watermelon-costed-more-orange

Abhishek Maheshwari, you should have gone to Specsavers

Anhishek dude, you should’ve gone to Secsavers.

It does not mention that the ORANGE is $9 more than the APPLE

Better question:

My friends all understand this question and the solution but I do not. I eat a bruised apple and go for counselling and score As for art lessons. Who is the worst people/person alive, me or my friends?

This is exactly what I think of the question. I can’t make sense of it. People say I should because I’m in advanced class BUT IT HAS NOTHING TO DO WITH THIS