1. The lowest different amounts of money in each pocket would be 1-10. 1+2+3+4+5+6+7+8+9+10=55, which is already 10 over her amount of money, so it would be impossible to fill all 10 pockets with different amounts.
You would need at least 55 coins to fill each pocket with a different amount of money.
2. This is impossible because if you add the height of each block you will get 55. 55 is an odd number, making it impossible to make two towers of the same height. If the heights of the blocks added together equal an even number, then you will be able to make two towers of the same height.
To make the two towers, n can equal 3,4,7,8,11,12,15,16,19,20 and all the other numbers in this pattern.
3. (4n+6)=(n+(n+1)+(n+2)+(n+3)). This means that the first number in the consecutive sequence will be multiplied by 4, but then 6 will be added, meaning that the numbers in the sequence added up will never be a multiple of 4.