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### Schools Mathematics Grand Challenge

PROBLEM 1

You have two squares. The lengths of their sides are whole numbers of cm. The total area of the two squares is 34 square cm. If you make a rectangle using two sides from one square and two sides from the other, what would its area be?

PROBLEM 2

A teacher picks two consecutive whole numbers between 1 and 5. She tells John what one of the numbers is and tells Sheila the other one. John and Sheila then have the following conversation:

John: I do not know your number.
Sheila: I do not know your number.

What number was given to Sheila?

Hint: consecutive numbers are beside one another, so 8 and 9 are consecutive but 10 and 12 are not.

PROBLEM 3

Back to wine gums! A bag contains 28 red, 31 green, 36 black, 29 orange and 27 yellow wine gums. Michael has been blindfolded so that he cannot see into the bag. What is the least number of wine gums that Michael must choose from the bag to guarantee that he has chosen at least THREE of the same colour?