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?

The required number of pretzel sticks possessed by each of the 10 people joining the individuals is 249.

Posted by K Sengupta on 2022-07-05 23:38:02