Random Puzzles 

Workings

Hint
This is a well known nursery rhyme.

Answer
AJCTA.

These are the initial letters from the nursery rhyme 'Jack and Jill went up the hill'. The letters represent 'and Jill came tumbling after'.

Workings

Hint
There are many answers, however, Z doesn't appear very often.

Answers
Choose from: luxury, struts, stylus, syrupy, trusts, twisty.

Other less common words include: scuzzy, syrups, syzygy, trouty, trusty, tryout, trysts.

Workings

Hint
Try working backwards.

Answer
£98.82.

Reasoning
At the end I was left with £32.94, which was half of my remaining money, so before buying the trousers I must have had £65.88.

Again, this was half of my money, so before buying the jacket I must have had £131.76 at the start.

As I now had £32.94 remaining, I must have spent £98.82.

Double-Checking
I started with £131.76, and I spent £65.88 on a new jacket, and then £32.94 on the trousers, a total spend of £98.82.

Workings

Hint
How many 1 x 1 squares are there, how many 2 x 2, …?

Answer
2,870 squares.

Reasoning
We have squares sizes from 1 x 1 up to 20 x 20, and these are the counts:
 1 x  1 = 400
 2 x  2 = 361
 3 x  3 = 324
 4 x  4 = 289
 5 x  5 = 256
 6 x  6 = 225
 7 x  7 = 196
 8 x  8 = 169
 9 x  9 = 144
10 x 10 = 121
11 x 11 = 100
12 x 12 =  81
13 x 13 =  64
14 x 14 =  49
15 x 15 =  36
16 x 16 =  25
17 x 17 =  16
18 x 18 =   9
19 x 19 =   4
20 x 20 =   1

Total = 400 + 361 + 324 + 289 + 256 + 225 + 196 + 169 + 144 + 121 + 100 + 81 + 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 = 2870.