coverPlease do NOT post your answer, but do say if you think you have solved the puzzle and how long it took. Solution on Monday.

You and a friend have a pile of 15 pennies and decide to play a little game. You will each take turns removing pennies from the pile.  On each turn you or your friend can take  1, 2, or 3 pennies. The loser is the person who takes the last penny.  You are allowed to go first. How many pennies should you take?

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.

43 comments

  1. took me about a minute. At least with this one, if my thinking was defective, I’ve still got a 1 in 3 chance of being right.

    1. “Please do NOT post your answer, but do say if you think you have solved the puzzle and HOW LONG IT TOOK [my capitals].”

      Probably took me about a minute, which by others’ standards, probably isn’t showing off (and could still be wrong).

  2. anyone who claims to have solved the game of nim in seconds without looking up the solution is not being very honest

  3. Took me a few minutes (OK Anonymous I know you are not interested). I’m quite pleased as I have seen this type of puzzle before but not worked out how to do it.
    BTW, for the benefit of Mr Colin Barnes, I should point out that I assumed that each penny was perfect with equally perfectly sharp corners.

  4. I can remember how to win when there are 15 matches to draw from, it didn’t take too long to check that it was the same for pennies,

  5. Took me a minute or two to brute force it, but I’m curious about whether there’s an algorithm which would make it easy to figure out strategies for different starting counts and number of coins which can be taken on a turn.

    1. there is, Martin Gardner published it half a century ago in Scientific American, reprinted in one of his books on recreational mathematics. the game is called Nim if you want to google it

  6. I’ve been puzzling over this one for hours and I’ve got nowhere .Anyone who gets this is a better man than I am.

  7. I didn’t time it but it didn’t take long. I’d seen similar (well the same actually, only with thirty coins) so just had to remember the rule to solve the puzzle.

    1. Aahh! the Non-Nim Dim Sum Sum game, 15 of the beauties on a table and I challenge you to take one.

  8. Well, posting an answer (e.g., “2 coins”) is not really helping in solving the problem or understanding the winning strategy this time, you still need to know how to proceed in the next steps of the game to win, i.e., the correct first step is not a guarantee that one will win. It took me about a minute to figure out the solution but now know the answer for N initial coins.

  9. Wasted at least an hour of my time (oh, ok, my employer’s time) but finally got the winning strategy. I thought this was perfect level of difficulty.

  10. my ans is to take one coin. this leaves the maximum no of rounds for my friend to make a mistake. this pzzle is very simple.

  11. Ahh… The Kobayashi Maru test. We change the parameters of the test and take 14 coins, thus leaving one for the opponent who then loses by taking the last coin.

  12. Just over six minutes. I laid out 15 one-sided Q-tips. I pointed the end toward or away depending on if I planned to take them or my imaginary enemy. I pointed the first toward me and the last toward him, then adjusted the rest until I figured it out. Maybe not the fastest solution, but it was fun. Thanks Richard!

  13. Took a few minutes. I had to work it out on paper. Started trying to lay out a tree to enumerate all the possibilities, then I realized I didn’t need to do that and found a quicker path to the answer.

  14. I took about 5 minutes of thinking about it, and another 5 minutes of checking. Then I realised what the trick was. I started by thinking what would one do if one started with 2, 3 or 4 coins instead of 15, and soon realised there was a pattern.

    It would be a good game for an adult to play against a child; allowing the child to go first still gives the adult an advantage if the child doesn’t know the trick – and you can work out how to let the child win if necessary.

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