MathDB

a) A game for two. The first player writes two rows of ten numbers each, the second under the first. He should provide the following property: if number

b

is written under

a

, and

d

-- under

c

, then

a + d = b + c

. The second player has to determine all the numbers. He is allowed to ask the questions like "What number is written in the

x

place in the

y

row?" What is the minimal number of the questions asked by the second player before he founds out all the numbers?
b) There was a table

m\times n

on the blackboard with the property: if You chose two rows and two columns, then the sum of the numbers in the two opposite vertices of the rectangles formed by those lines equals the sum of the numbers in two another vertices. Some of the numbers are cleaned but it is still possible to restore all the table. What is the minimal possible number of the remaining numbers?

Problem Statement