2

Part of 2016 Auckland Mathematical Olympiad

Problems(2)

2 player game with divisors of 328 (2016 Auckland MO J2)

Source:

328

is written on the board. Two players alternate writing positive divisors of

328

on the board, subject to the following rules:

\bullet

No divisor of a previously written number may be written.

\bullet

The player who writes 328 loses. Who has a winning strategy, the first player or the second player?

number theorygamecombinatorics

computational, equal angles and a square (2016 Auckland MO S2)

Source:

ABCD

\overline{AC}

\overline{BD}

E

F

\overline{CD}

\angle CAF = \angle FAD

\overline{AF}

\overline{ED}

G

\overline{EG} = 24

cm, then find the length of

\overline{CF}

geometryequal anglessquare