perplexus.info :: Numbers : Cross Product Quickie

Cross Product Quickie (Posted on 2023-04-24)

+---+     +---+     +---+
|   |  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)?

See The Solution Submitted by K Sengupta

Rating: 3.3333 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

Correct Solution (spoiler)

| Comment 4 of 6 |

I couldn't to it in my head, but it is easy enough to do on paper. Took 2 to 3 minutes.

Let the squares be

abc

def

ghi

i = 7, as only row 3 and column 3 are divisible by 7.

e = 5, as only row 2 and column 2 are divisible by 5.

b = 9, as only row 1 and column 2 are divisible by 9.

Then h = 4, so that 9*5*4 = 180

Then g = 2, so that 2*4*7 = 56

Then a, c, and f cannot be 8, so d = 8.

The rest falls into place.

Final correct solution:

691

853

247

Edited on April 26, 2023, 9:45 am

Posted by Steve Herman on 2023-04-24 09:05:56

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