+---+     +---+     +---+
|   |  X  |   |  X  |   | = 54
+---+     +---+     +---+
  X         X         X
+---+     +---+     +---+
|   |  X  |   |  X  |   | = 120
+---+     +---+     +---+  
  X         X         X
+---+     +---+     +---+
|   |  X  |   |  X  |   | = 56
+---+     +---+     +---+
  =         =         =
 96        180       21

Use each of the digits from 1 to 9 exactly once to satisfy this cross product puzzle.
How fast can you come up with the solution using only p&p (no calculator)?

Extra Challenge: Can you come up with the solution in your mind (without using p&p)?

Done mostly in my head, as far as math goes, but not with respect to memory.  I would record answers as I found them.

Call the digits:
ABC
DEF
GHI

If 21 has 3 factors, one of them must be a 1.
{C,F,I} are {1,3,7}
54 is 6*9, factors are 2,3,3,3; but can't be 3, so,
{A,B,C} are {1,6,9}
120 does not contain 7 as a factor
C = 1
F = 3
I = 7
G*H = 8, so {G,H} = {2,4}
If B were 6, then E*H = 30 = 5*6, but 6 was already used, therefore
B = 9
A = 6, therefore D*G = 16, or {D,G} = {2,8}

{G,H} = {2,4}
{D,G} = {2,8}  so G=2, D=8, H=4
Remaining cell, E=5

691
853
247

Posted by Larry on 2023-04-24 10:04:01