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 Pretzel sticks (Posted on 2003-09-22)
I have lots of pretzel sticks. I eat 3 of the pretzel sticks before somebody comes and joins me. When he arrives I eat three more sticks and then divide the rest equally between the two of us. The piles come out equally, but just as I am done dividing up the piles between the other person and me, another person joins us.

I combine the piles and divide them up for 3 people, again eating 3 pretzel sticks before doing so. The piles come out equally again.

But before anyone has a chance to eat any of them, another person comes. So I combine all the piles, eat 3 pretzel sticks, and divide them up among the 4 of us.

People keep coming in this fashion until there are 10 piles (including mine), and then nobody comes once there are 10 piles, so we all eat our pretzel sticks. I am happy that the piles came out evenly each time, and note that I have the least amount of pretzel sticks that this would happen with.

How many pretzel sticks did the people who joined me have (individually), and how many pretzel sticks would I have had if I didn't share them with anybody?

 Submitted by Gamer Rating: 3.3333 (3 votes) Solution: (Hide) To solve this problem, the number of pretzels is: 6 more than a multiple of 2, 9 more than a multiple of 3, 12 more than a multiple of 4, up to 30 more than a multiple of 10. To find that number, just take the LCM of 2,3,4,5,6,7,8,9, and 10, which is 2520, and subtract 3. This means I had 2517 pretzel sticks. 2517 is 1*2517 2514 is 2*1257 2511 is 3*837 2508 is 4*627 2505 is 5*501 2502 is 6*417 2499 is 7*357 2496 is 8*312 2493 is 9*277 2490 is 10*249 So, each of the other nine people ended up eating 249 pretzels. I ate 279 pretzels, after adding on the 3 that I ate each time!

 Subject Author Date Explanation to Puzzle Answer K Sengupta 2022-07-06 22:05:47 Puzzle Answer K Sengupta 2022-07-05 23:38:02 re:Charlie's solution Lee 2003-09-23 09:19:13 solution gabbo 2003-09-22 19:09:26 solution Charlie 2003-09-22 13:27:43

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