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1. Sinead's pockets
Imagine you have ten pockets. The minimum you can have in a pocket is 1. The minimum you can add on to make the amounts different is 1. So if you add 1 to each pocket each time, by the time you reach your 10th pocket, you would need 11 pound coins more than 44, which is 55. Therefore, the minimum is 55.
2.Cube towers
It is impossible to build a tower of equal height using cubes with sides of n(1 to 10)cm because the total of these numbers (55) divided by two would give you a decimal (27.5). All of the cube sides are whole numbers which can't be added to make a decimal.
2a.
To make two towers of equal height using blocks with consecutive side lengths, you would need four blocks with sides of n(1 to 4).
Tower 1:3+2
Tower 2:1+4
3.Totals of consecutive numbers
It is impossible to take four consecutive numbers, to total them and to get a multiple of four. Imagine you have an unknown value, lets call it 'x'. Each of the consecutive numbers are; x, x+1, x+2, x+3. For example: 10=x, 11=x+1, 12+=x+2,13=x+3. If you add the numbers 1, 2 and 3, you get six which isn't a multiple of 4. If the numbers were just x, x, x and x each time, it would always be a multiple of four. However, that six you add on prevents the number from becoming a multiple of 4.