If you are in or around Cheltenham, I am doing a few events at the science festival there this weekend, including some seances and a talk with Jon Ronson.  Hope you can make it.

As I said at the beginning of the week,  I have a rare set of 1960s magic magazines on Ebay right now – details here.  I noticed that one of the magazines has a neat puzzle in it, so it seemed appropriate to use as the basis for this week’s puzzle….

A friend of mine has £100 in a bank account.  Whenever he takes out money he records how much he has taken out and the balance.  Here are his accounts for last week….

WITHDRAWN                                BALANCE

40                                                      60
30                                                      30
20                                                      10
9                                                        1
1                                                         0

There is one small problem – the WITHDRAWN column adds up to 100, but the BALANCE column adds up to 101 – how can this be the case?

As ever, please do NOT post your solutions, but do feel free to say if you have solved it and how long it took.  Answer on Monday.

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 USA here). You can try 101 of the puzzles for free here.

94 comments

  1. This seems like an overly simplified version of the 3 men checking into a hotel and 30 doesn’t equal 29 problem.

    1. OK, I missed that, but as I mentioned, the book I have is from the 50s, and I’m guessing it was old even then

  2. Can I not leave a comment as a guest?

    This seems like an overly simplified version of the 3 men checking into a hotel and 30 doesn’t equal 29 riddle.

  3. Often I struggle for hours with these questions, today’s was so easy, it took the time it took to read the question.

  4. Less of a puzzle (it isn’t one) – more of (yet) another advert for Richard’s various financial exploits!

  5. 0.05 milliseconds, look at the size of my d***!

    Although the willy waving now seems to be more focussed how quick people can reply with a fatuous comment rather than how long they claim it took them to solve the puzzle/book advert.

    Next Friday I’m getting up an hour earlier.

    1. It’s not the fact that they’re posting their times so much as the fact that so many answers always seem to range from “instantly” to “5 seconds.” Admittedly, some of them (today’s, for instance), can be solved that fast if one has an idea of what the “trick” is, but I have a suspicion that there’s also a lot of exaggeration going on.

  6. Well I’m so clever that upon seeing that Richard had put a set of The Cauldron on EBay FOUR DAYS AGO, I anticipated that he would be using a puzzle from one of them for his Friday puzzle feature. I quickly managed to get hold of the set, and researched each until I selected this very puzzle. I instantly knew the answer with just the most casual of glances at it. I did all this while simultaneously wrestling a lion and learning Cantonese (it was a Monday after all). I would have posted this earlier of course but I was just finishing giving my wife her fifth orgasm of the day. So I guess I did the puzzle in approximately MINUS FOUR DAYS. Now when one of you maggots can claim this, I’ll look you in the eye and salute you like the man I am, but till then, keep trying.

    1. Except that it’s much older than any issue of The Cauldron. I have it in a book by Martin Gardner from the 50s. In fact, I have seen several of these puzzles in that book

    1. Ok, so it’s now at 101. Do some more transactions and make it add up to 100. This will be interesting.

    2. Obviously if it’s already 101 it can’t become any less, but the statement was “never”.

      WITHDRAWN BALANCE
      1 99
      98 1
      1 0
      ———————————–
      100 100

    3. Yes, however many times you change the balance, it will NEVER add up to 100.

      Hope this helps.

    4. If you only withdraw money as specified in the puzzle then the withdrawn column will ALWAYS add up to the amount withdrawn. Even if you do not then both columns can still add to 100, your point is irrelevant and wrong.

      60…..40
      -1……41
      22…..19
      19……0

  7. *blink* As others have said, there’s no puzzle in the maths. The puzzle is really “why do you expect a £100 answer, and therefore why are you asking why it’s not £100?”

  8. That was a rubbish maths puzzle. Here is a much better one:

    Three guests check into a hotel room. The clerk says the bill is $30, so each guest pays $10. Later the clerk realizes the bill should only be $25. To rectify this, he gives the bellhop $5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guests didn’t know the total of the revised bill, the bellhop decides to just give each guest $1 and keep $2 for himself.

    Now that each of the guests has been given $1 back, each has paid $9, bringing the total paid to $27. The bellhop has $2. If the guests originally handed over $30, what happened to the remaining $1?

  9. Oh the wonder of maths… reminds me of the farmer who had 17 cows, and on his death bequeathed half to one child, a third to the second, and a ninth to the third. Since 17 is divisible by neither two, three or nine the children were faced with a puzzle… until a neighbouring farmer came along and lent them one of his cows…

  10. Is Holden right – is the incredulity expressed just a way for people to show off how clever they are?

    In case anyone is honestly puzzled, here’s the “Puzzle Purpose for Dummies” summary:

    (1) Many people do puzzles to hone their thinking skills.
    (2) A common way people sometimes mislead us is to covertly smuggle bad assumptions into their definitions of a problem.
    (3) By working through such problems and discovering the bad assumptions, we get better at spotting such fallacies.

    Now, I suspect that none of the showing-off crowd was born being able to see through such misdirections as the one in this puzzle. I sure wasn’t. Although I noticed the fallacy here rather quickly, it’s only because I’d seen similar problems in the past.

    Thanks, Richard, for not forgetting those people who are still beginning their journey to puzzle-cracking expertise.

    1. Hear hear, well said and, a new one, which I hope will catch on in these circles, let he who is without (any past history of even a temporary confusion over) sin (cos and tan) cast the first stone.

  11. Wow, lots of people spoiling the answer this week. Is it really so hard to simply say that you thought it was easy, and wait a few days before revealing the answer?

  12. Holden and Timothy,

    Dr Richard Wiseman states on his blog “As ever, please do NOT post your solutions, but do feel free to say if you have solved it and how long it took.”

    I think that’s what most people responding to this question have done.

    Yes – 1 second!

  13. As a slight extension to the puzzle:

    What are the smallest and largest possible values for the sum of the balances, assuming:
    (a) his initial balance is £100,
    (b) a five day week,
    (c) he is left with a zero balance,
    (d) he never deposits any money during the week,
    (e) he must draw a (non-zero) amount each day, and
    (f) he can draw only a whole number of pounds on each day?

    1. I get 10 as the lowest value, but I get 4950 as the highest value. None of the a-f rules say there can only be one withdrawal per day

    2. Actually, I get even more. 499950

      Point f says each day’s withdrawal must be an integer, but each withdrawal could be a penny (disregarding the fact that no bank would allow such a small withdrawal – they’d probably balk at a pound too), so I withdraw one penny an even multiple of 100 times per day until the bank account is empty.

    3. Good spot, Anders!

      I should amend (e) to read:
      he must draw exactly one (non-zero) amount each day.

      However, (f) does say he can draw only a whole number of *pounds*, which rules out your second answer.

    4. If you change (e) that way, then I agree that 390 is the max.

      On your second point though, it says can only draw a whole number of pounds *on each day*, which leaves open the possibility of multiple penny withdrawals, as long as they add up to a whole number of pounds at the end of the day 🙂

      But yes, if you modify (e) it makes it harder to violate the rules 🙂

    1. “I don’t get it. Who adds up bank balances anyway?”

      People who want to work out an average balance maybe. Can’t see any other reasons.

  14. a lot of chat for not much puzzle,
    perhaps the extra pound in this puzzle is the missing one from the diners/waiter confusion.

  15. Amazing – the sum of what’s left is not equal to the sum of what’s taken. (This is becuase you need to include the 20p fee on each withdrawal 😉 ). (Banks have to make their money somehow)

  16. Timothy, you made some good points. I, too, suspect that many of those who pride themselves in knowing the answer before they even finish reading the puzzle probably recognize the pattern of a familiar puzzle. So there.

  17. There is no need to add the £1, just as there would be no need to add the £100 (starting balance) otherwise it would add up to £201.

  18. was wondering for 5 mins, how could that be possible. But then it struck me about the cumulative affairs. ‘Another richard’ gave the best explanation – what would happen had we withdrawn $1 at a time.

    -vishal garg

  19. Pingback: math for kids

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