median
don steward
mathematics teaching 10 ~ 16

Saturday, 12 February 2011

impossibilities

(1) Sinead has 10 pockets and 44 one pound coins
she wants to put all these pounds into her pockets so that each pocket contains a different number of coins

she could have 0 in one pocket

prove that this impossible

(2) Abbie has a set of 10 plastic cubes. The edges go up in 1 cm steps, starting from a 1 cm cube (the largest being a 10 cm cube). She tries to build two towers of the same height using all of the cubes...

prove that this impossible

(3) Eustace wants to end up with a number in the 4 times table by adding any four consecutive numbers

prove that this is impossible

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