I found this brainteaser in a Sunday newspaper many years ago, I can't remember which one. It provides a good example of problem solving thought, I think.
"You see, Inspector, the combination of my safe is a six figure number. In case anyone needed to get into it while I was away, I gave each of my clerks (Atkins, Browning and Clark) one of the two figure numbers which make up the combination. I also told each the position in the combination of the number of another clerk, but not the number itself.
Browning must have overheard me telling a friend that it is a coincidence that two of the numbers are squares, and that if you put them together you get a four figure number that equals the other clerk's number squared. I remember I also said something about whether or not the combination is divisible by this clerk's number.
When he was caught, Browning said, 'I canft understand why the alarm went off: I know Clark's is the first number!' I later realised that what Ifd told my friend about whether or not the number was a factor was wrong, which was lucky for me as Browning had got his own number in the right place."
What is the combination of the safe?
Clearly a table of squares might help, and I have posted one below! Can you solve the problem?
| Number | Square | Number | Square | Number | Square | Number | Square | |||
| 1 | 1 | 26 | 676 | 51 | 2601 | 76 | 5776 | |||
| 2 | 4 | 27 | 729 | 52 | 2704 | 77 | 5929 | |||
| 3 | 9 | 28 | 784 | 53 | 2809 | 78 | 6084 | |||
| 4 | 16 | 29 | 841 | 54 | 2916 | 79 | 6241 | |||
| 5 | 25 | 30 | 900 | 55 | 3025 | 80 | 6400 | |||
| 6 | 36 | 31 | 961 | 56 | 3136 | 81 | 6561 | |||
| 7 | 49 | 32 | 1024 | 57 | 3249 | 82 | 6724 | |||
| 8 | 64 | 33 | 1089 | 58 | 3364 | 83 | 6889 | |||
| 9 | 81 | 34 | 1156 | 59 | 3481 | 84 | 7056 | |||
| 10 | 100 | 35 | 1225 | 60 | 3600 | 85 | 7225 | |||
| 11 | 121 | 36 | 1296 | 61 | 3721 | 86 | 7396 | |||
| 12 | 144 | 37 | 1369 | 62 | 3844 | 87 | 7569 | |||
| 13 | 169 | 38 | 1444 | 63 | 3969 | 88 | 7744 | |||
| 14 | 196 | 39 | 1521 | 64 | 4096 | 89 | 7921 | |||
| 15 | 225 | 40 | 1600 | 65 | 4225 | 90 | 8100 | |||
| 16 | 256 | 41 | 1681 | 66 | 4356 | 91 | 8281 | |||
| 17 | 289 | 42 | 1764 | 67 | 4489 | 92 | 8464 | |||
| 18 | 324 | 43 | 1849 | 68 | 4624 | 93 | 8649 | |||
| 19 | 361 | 44 | 1936 | 69 | 4761 | 94 | 8836 | |||
| 20 | 400 | 45 | 2025 | 70 | 4900 | 95 | 9025 | |||
| 21 | 441 | 46 | 2116 | 71 | 5041 | 96 | 9216 | |||
| 22 | 484 | 47 | 2209 | 72 | 5184 | 97 | 9409 | |||
| 23 | 529 | 48 | 2304 | 73 | 5329 | 98 | 9604 | |||
| 24 | 576 | 49 | 2401 | 74 | 5476 | 99 | 9801 | |||
| 25 | 625 | 50 | 2500 | 75 | 5625 | 100 | 10000 |