Is HP42 smarter than a kid on TV?

[Valentin Albillo]

(04-30-2018 09:09 AM)RMollov Wrote:  

(04-28-2018 10:18 PM)Valentin Albillo Wrote:  The kid just needs to remember *one* 5x5 magic square formed by the numbers 1 to 25 (which is very easy because of the symmetries, no need to remember the contents of the 25 locations),

Would you elaborate a bit more on the bolded?
I'd like to know how to do that.

This is the very magic square the kid uses as a basis, later adding the computed constant to all its elements. First notice this easy-to-remember Z pattern along the diagonal:

10-11-12-13-14-15-16:

17  24   1   8  15
23   5   7  14  16
 4   6  13  20  22
10  12  19  21   3
11  18  25   2   9

This takes care of 7 numbers (by the way, the central element, 13, is simply the magic constant (65) divided by the order of the square (5): 65/5 = 13).

Next notice the patterns in the smaller diagonals:

4-5-6-7-8:

17  24   1   8  15
23   5   7  14  16
 4   6  13  20  22
10  12  19  21   3
11  18  25   2   9

and 18-19-20-21-22:

17  24   1   8  15
23   5   7  14  16
 4   6  13  20  22
10  12  19  21   3
11  18  25   2   9

This already takes care of the locations of 17 of the 25 numbers and the remaining 8 also belong to patterns (2,3, ... , 23,24, etc.)

Notice also that all elements placed symmetrically in respect to the center one add up to 26. For instance, the four corners 17 and 9 (17+9=26), 15 and 11 (15+11=26), and all the rest too (24+2, 1+25, 8+18, 4+22, 10+16, etc), so you'd only need to remember half the locations plus the fact that 13 is the center one (as explained before).

In short, the whole 5x5 magic square can be remembered with very minimal effort after memorizing a few patterns and the symmetry x+x' = 26. After a little practice you'll get the hang of it.

V.
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