Brain teasers based on Bezout’s identity — RMO training

Problem 1.

In a special football game, a team scores 7 points for a touch-down and 3 points for a field goal. Determine the largest mathematically unreachable number of points scored by a team in an (infinitely) long game.

Problem 2.

There is an ample of supply of milk in a milk tank. Mr. Fat is given a 5 litre (unmarked) container and a 9-litre (unmarked) container. How can he measure out 2 litres of milk?

The above two are classic brain teasers based on Bezout’s identity.

More later,

Nalin Pithwa