Clocking question?

Question

There are n children seated in a circle on the floor. The teacher walks behind the children in a clockwise direction with a box of candies. Starting from a given child, she drops a candy behind this child. She then skips one child and drops a candy behind the next child. Now, she skips two children and drops a candy behind the next child. She continues in this way, at each stage skipping one child more than at the preceding stage before dropping a candy behind the next child.

(a) For n = 4,5,6,7,8 determine which children will have been given candies and the corresponding number of candies given at the 9th stage.

(b) For those values of n in (a) above, which children do you think will never receive any candy? Prove it mathematically.

Can anyone pls help? Thanks!

Answer 1

thge kids that gets a candy are caractreised by the following :

1,3,6,10,15 etc ( Cn+1 = Cn + n)
where C a child n the childs index.

because sghe can walk multiple tours you have to take the modulo n to get the proper child's index.

so for 4 kids : 1,3,2,2,3,1...

Answer 2

(a)
for n=4 ;kids 1 and 3 will get candies
n=5 ; kids 1,3 will get candies
n=6 ; kids 1,3,6 will get candies
n=7 ; kids 1,3,6 will get candies
n=8 ; kids 1,3,6 will get candies
n=9 ; kids 1,3,6 will get candies

(b)
for n=4 ; kids 2,4 will never get
for n=5 ; kids 2,4,5 will never get
for n=6 ; kids 2,4,5 will never get
for n=7 ; kids 2,4,5,7 will never get
for n=8 ; kids 2,4,5,7,8 will never get
for n=9 ; kids 2,4,5,7,8,9 will never get