1

Part of 2015 CHMMC (Fall)

Problems(2)

2015 Fall Team #1

Source:

3

players take turns drawing lines that connect vertices of a regular

n

-gon. No player may draw a line that intersects another line at a point other than a vertex of the

n-

gon. The last player able to draw a line wins. For how many

n

4\le n \le 100

does the first player have a winning strategy?

combinatoricsgeometry

2015 CHMMC Tiebreaker 1 - 2015- cube-invariant postitive integers

Source:

Call a positive integer

x

n

-cube-invariant if the last

n

x

are equal to the last

n

x^3

1

n

-cube invariant for any integer

n

2015

-cube-invariant numbers

x

are there such that

x < 10^{2015}

CHMMCnumber theorylast digitsDigits