Please 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.

1. Finally an easy one. Took about 15 seconds.

2. Walter says:

3. BenFriman says:

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. Anonymous says:

Nob

4. Anonymous says:

no one cares how much time it took you guys.

1. Hugh Jarse says:

Hey Anonymous, if you want to comment could you at least do so using correct English

5. Eddie says:

It should say “On each turn you *and* your friend can take 1, 2, or 3 pennies.”

6. Eddie says:

Had no idea how/time to do this. Looked up the answer and it’s very clever.

7. Anonymous says:

yeh no one cares so why do u all hav to showoff?

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).

8. Tom Cook says:

Got it in 2 mins.

9. Anders says:

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

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.

11. Lazy T says:

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,

12. I have one answer but have not checked if I is right or not!

13. 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.

14. mightyhero says:

Too easy.

1. Anders says:

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

15. Anonymous says:

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.

16. Stevie. says:

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.

17. Miss Chili says:

Ah, yes. The Nim-Sum game, which is a bit different to the zero-sum game 😀

1. Segway Drivin' Troll (in da hood) says:

..and indeed different from the Dim Sum game…..

2. Lazy T says:

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

18. Princess says:

Easy one, already know how to find the answer for any number of pennies and any number of picking

19. 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.

20. chivvy says:

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.

21. Dharmaruci says:

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.

22. Got it in less than a minute 🙂

23. Phil H says:

Nice n easy. 15 seconds after 4 beers

24. KevinM says:

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.

25. 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!

26. rmb says:

5 minutes

27. Took about a minute. This one didn’t require any out-of-box thinking… just a math problem.

28. Anonymous says:

easy

29. Gus Snarp says:

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.

30. Paul Durrant says:

Solved in less than a minute.

31. Chris says:

Solved it by working backwards from the 1 coin remaining at his turn.

32. 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.

33. John says:

I got the answer but it all depends on who your friend is.

34. Less than a minute — my first strategy had my opponent winning, but I caught the error.

35. Anonymous says:

Three and a half months.