Brainteaser

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 canft understand why the alarm went off: I know Clark's is the first number!' I later realised that what Ifd 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?



NumberSquare       NumberSquare       NumberSquare       NumberSquare
11       26676       512601       765776
24       27729       522704       775929
39       28784       532809       786084
416       29841       542916       796241
525       30900       553025       806400
636       31961       563136       816561
749       321024       573249       826724
864       331089       583364       836889
981       341156       593481       847056
10100       351225       603600       857225
11121       361296       613721       867396
12144       371369       623844       877569
13169       381444       633969       887744
14196       391521       644096       897921
15225       401600       654225       908100
16256       411681       664356       918281
17289       421764       674489       928464
18324       431849       684624       938649
19361       441936       694761       948836
20400       452025       704900       959025
21441       462116       715041       969216
22484       472209       725184       979409
23529       482304       735329       989604
24576       492401       745476       999801
25625       502500       755625       10010000