2

Part of 2014 Tournament of Towns.

Problems(2)

TOT 2014 Spring O J2, 15 pasties on a round plate in a circular way

Source:

15

pasties. She placed them on a round plate in a circular way:

7

7

with meat and one with cherries in that exact order and put the plate into a microwave. All pasties look the same but Olga knows the order. However she doesn't know how the plate has been rotated in the microwave. She wants to eat a pasty with cherries. Can Olga eat her favourite pasty for sure if she is not allowed to try more than three other pasties?

TOT 2014 Spring A J2, two player game in 5x5 board

Source:

Peter marks several cells on a

5\times 5

board. Basil wins if he can cover all marked cells with three-cell corners. The corners must be inside the board and not overlap. What is the least number of cells Peter should mark to prevent Basil from winning? (Cells of the corners must coincide with the cells of the board).

gamecombinatoricssquare table