3

Part of 2014 CHMMC (Fall)

Problems(2)

2014 Fall Team #3

Source:

Suppose that in a group of

6

A

is friends with

B

B

is friends with

A

. If each of the

6

people draws a graph of the friendships between the other

5

people, we get these

6

graphs, where edges represent friendships and points represent people. https://cdn.artofproblemsolving.com/attachments/5/5/7265067f585e3dfe77ba94ac6261b4462cd015.png If Sue drew the first graph, how many friends does she have?

2014 CHMMC Tiebreaker 3 - 2 players- game on a pile of n beans

Source:

Two players play a game on a pile of

n

beans. On each player's turn, they may take exactly

1

4

7

beans from the pile. One player goes first, and then the players alternate until somebody wins. A player wins when they take the last bean from the pile. For how many

n

2014

2050

(inclusive) does the second player win?

combinatoricsnumber theoryCHMMC