The numbers from 1 to 100 are arranged, snaking back and forth from the bottom, in a 10x10 grid:

100 99 98 97 96 95 94 93 92 91

 81 82 83 84 85 86 87 88 89 90

 80 79 78 77 76 75 74 73 72 71

 61 62 63 64 65 66 67 68 69 70

 60 59 58 57 56 55 54 53 52 51
+--------------+
|41 42 43 44 45|46 47 48 49 50
|              |
|40 39 38 37 36|35 34 33 32 31
|              |         
|21 22 23 24 25|26 27 28 29 30
|              |         
|20 19 18 17 16|15 14 13 12 11
+--+           |
| 1| 2  3  4  5| 6  7  8  9 10
+--+-----------+

Marked off are two subsquares that, if you add up the numbers within them, the total is the square of one of the numbers within. The larger square (5x5) totals 625, the square of 25, which is found within that marked square. The other one shown is the trivial "1", a 1x1 square, the single number in which of course is its own square.

Find another subsquare where the sum of its contained numbers is equal to the square of one of those numbers.

Let me read Charlie's chart as A to J across and 1 to 10 down.

Let me define the squares to which I refer as being lowest values top left corner of the range while the others are at the other extreme,
ie;
[A1] represents 100
[A1:B2] holds (100,99,81,82)


That said, these beautiful fit Charlie's requirements but the root value does not lie within his definition:

[A5:E9]    = 900; sqrt = 30
[A6:E10]  = 625; sqrt = 25
[F6:H8]    = 324; sqrt = 18
[F8:H10]  = 144; sqrt = 12

However there is something missing, one that coincides with a significant ancient Roman calendar date which I'm not divulging here.

I enjoyed the challenge Charlie but thought it different to address this from the perspective which I had suggested when under review; you didn't take that on board being your perogative but I am adding those in for further thought.

I think, back then (prior para ref.) my thought was to challenge for squares where the base value lay outside your defined area.

Edited on May 21, 2008, 11:18 am

Posted by brianjn on 2008-05-21 11:05:49