10 pockets and £40: The smallest amount of coins he could have, having a different amound in each pocket, would be having 1 in the first pocket, 2 in the second and so on until he has got to 10. If you add all those up, 1+2+3+4+5+6+7+8+9+10=55, makes more then 44 which is the amount of coins that he had. So it is not possible for him to have a different amount of coins in each pocket that add up to 44.
Plastic cubes: This is impossible because if you just make one big tower with all the cubes,1+2+3+4+5+6+7+8+9+10=55, it equals 55. Abbie wants 2 equal towers with all those cubes and 55 does not divide into a whole number so she can not make 2 equal towers.
n plastic cubes: Starting from one, the first two will not be able to make a even tower but the second two will but the third two will not and this carrys on forever. For it to make two even towers the number of all the cubes added up will have to be even.
Consequtive numbers: If you add the first set of consequtive numbers, 1,2,3,4, it makes 10 which is not a multiple of 4 from then on each row of consequtive numbers will be 4 more then the last. None of these numbers will ever be a multiple of 4.