There are 8 possible combinations:
Cube |
Not cube |
|
| Square | 64 |
Lots of possibilities |
| Not square | 27, 125, 216, 343 |
Lots of possibilities |
Cube |
Not cube |
|
| Square | 729 |
Lots of possibilities |
| Not square | 512, 1000 |
Lots of possibilities |
Mr Jones says he knows that the number is one of two possibilities, so he must be thinking of the two perfect cubes between 500 and 1300 which are not square numbers.
Since Mr Smith lied about the size of the number and whether it was a square number or not, his house number must really be between 13 and 500, and both a square and a cube number.
Therefore his house number can only be 64
Perfect Squares |
Perfect Cubes |
27 |
|
16 |
64 |
25 |
125 |
36 |
216 |
49 |
343 |
64 |
512 |
81 |
729 |
100 |
1000 |
121 |
|
144 |
|
169 |
|
196 |
|
225 |
|
256 |
|
289 |
|
324 |
|
361 |
|
400 |
|
441 |
|
484 |
|
529 |
|
576 |
|
625 |
|
676 |
|
729 |
|
784 |
|
841 |
|
900 |
|
961 |
|
1024 |
|
1089 |
|
1156 |
|
1225 |
|
1296 |