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
During a recent police investigation, Chief Inspector Stone was interviewing five local villains to try to identify who stole the prize cake from the mid-summers fayre. Below is a summary of their statements:
Alex: it wasn't Emery
it was Billie
Billie: it wasn't Charlie
it wasn't Emery
Charlie: it was Emery
it wasn't Alex
Dale: it was Charlie
it was Billie
Emery: it was Dale
it wasn't Alex
It was well known that each suspect told exactly one lie. Can you determine who stole the cake?
Reasoning
Looking at Billie's statements, one of the statements was a lie and the other was the truth. Therefore, it must have been either Charlie or Emery.
Looking at Dale's statements, for the same reason, it was either Charlie or Billie.
Therefore, it must have been Charlie who committed the crime.
Double-checking this against the other statements confirms this.
?
Puzzle 4
Can you find a 5-digit number …
… whose digits add up to 18 and whose product is 210 and the digits increase from left to right in the number?
