When multiplying any two numbers, for example 15 * 18, the value is the same as:

x * y = avg(x,y)2 - (avg(x,y) - min(x,y))2
Which simplifies to:
x * y = 2 * avg(x,y) * min(x,y) - min(x,y)2

so 15 * 18 =
= avg(15,18)2 - (avg(15,18) - min(15,18))2
= 2 * avg(15,18) * min(15,18) - min(15,18)2
= 2 * 16.5 * 15 - 152
= 270

So the value of any multiplication is the same as the average of the two sides squared minus the distance from the numbers to the average squared.



For example (reload page for more random examples):

6 * 13 = 78
avg(6,13) = 9.5; min(6,13) = 6
9.52 - (9.5 - 6)2 = 78
2 * 9.5 * 6 - 62) = 78

-3 * 10 = -30
avg(-3,10) = 3.5; min(-3,10) = -3
3.52 - (3.5 - -3)2 = -30
2 * 3.5 * -3 - -32) = -30

-8 * 10.125 = -81
avg(-8,10.125) = 1.0625; min(-8,10.125) = -8
1.06252 - (1.0625 - -8)2 = -81
2 * 1.0625 * -8 - -82) = -81

13 * 7 = 91
avg(13,7) = 10; min(13,7) = 7
102 - (10 - 7)2 = 91
2 * 10 * 7 - 72) = 91

13 * 4.25 = 55.25
avg(13,4.25) = 8.625; min(13,4.25) = 4.25
8.6252 - (8.625 - 4.25)2 = 55.25
2 * 8.625 * 4.25 - 4.252) = 55.25

-2 * 7 = -14
avg(-2,7) = 2.5; min(-2,7) = -2
2.52 - (2.5 - -2)2 = -14
2 * 2.5 * -2 - -22) = -14

-10 * 1 = -10
avg(-10,1) = -4.5; min(-10,1) = -10
-4.52 - (-4.5 - -10)2 = -10
2 * -4.5 * -10 - -102) = -10