444

Part of 1987 All Soviet Union Mathematical Olympiad

Problems(2)

ASU 444 All Soviet Union MO 1987 Sea battle game, 7x7 table

Source:

The "Sea battle" game.
a) You are trying to find the

4

-field ship -- a rectangle

1x4

, situated on the

7x7

playing board. You are allowed to ask a question, whether it occupies the particular field or not. How many questions is it necessary to ask to find that ship surely?
b) The same question, but the ship is a connected (i.e. its fields have common sides) set of

4

square tablegamegame strategycombinatorics

ASU 445 All Soviet Union MO 1987 (n+2)/1^{1987} + 2^{1987} + ... + n^{1987}

Source:

1^{1987} + 2^{1987} + ... + n^{1987}

is divisible by

n+2

divisiblenumber theory