100 kids with 100 Sticks

[jeandrew37]

How would I begin to start this problem?


you have 100 kids
you have 100 sticks
you have limited prizes to be awarded among the 100 kids
to determine the number of kids getting prizes you
- line kids up 1-100

- the 1rst kid, including himself, gives all kids a stick

- the 2nd kid takes away the stick from himself and all even numbered kids

- the 3rd kid does two things, he takes away a stick from himself and any kid w/ multiple of 3 that has a stick BUT gives a stick to any kid having multiple of 3 that does not have a stick

- the 4th kid does the same thing as the 3rd kid, except for multiples of 4

- the process is continued up to the 100th kid



The number of prizes are equal to the number of kids having sticks at the end. Determine the number of sticks

 

[Deleted member 4993]

How would I begin to start this problem?


you have 100 kids
you have 100 sticks
you have limited prizes to be awarded among the 100 kids
to determine the number of kids getting prizes you
- line kids up 1-100

- the 1rst kid, including himself, gives all kids a stick

- the 2nd kid takes away the stick from himself and all even numbered kids

- the 3rd kid does two things, he takes away a stick from himself and any kid w/ multiple of 3 that has a stick BUT gives a stick to any kid having multiple of 3 that does not have a stick

- the 4th kid does the same thing as the 3rd kid, except for multiples of 4
That (the same thing as the 3rd kid) cannot happen! The third kid started with a stick in hand - so he put it away. The fourth kid will start with "no stick" in hand (2nd. kid took it away) - so there is nothing for him to put away!!

Does he instead pick up a stick?

- the process is continued up to the 100th kid



The number of prizes are equal to the number of kids having sticks at the end. Determine the number of sticks