July 2024
Problem of the Month
Pretzel Problem
Submitted by K. Sengupta of Calcutta, India
Mr. Richards has a number of pretzel sticks.
He eats 3 of the pretzel sticks before somebody comes and joins him.
When the guest arrives he eats three more sticks and then divides the rest equally between the two of them.
The piles come out equally, but just as Mr. Richards is done dividing up the piles between the other person and himself, another
person joins them.
He combines 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 Mr. Richards combines all the piles, eats 3 pretzel sticks, and divides them up among the 4 of them.
People keep coming in this fashion until there are 10 piles (including Mr. Richards'), and then nobody comes once there are 10 piles, so they all eat their pretzel sticks.
Mr. Richards is
happy that the piles came out evenly each time, and notes that he has the least amount of pretzel sticks with which this would happen.
How many pretzel sticks did each person who joined Mr. Richards have, and how many pretzel sticks would Mr. Richards have had if he didn't have to share them with
the guests?