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2-Row Number Grid (Posted on 2022-01-15) Difficulty: 3 of 5
The ten digits 0 through 9 are to be placed in the grid below so that:

  1. The product of A and B is the 2-digit number CD.
  2. The product of B and C is the 2-digit number DE.
  3. The three sums A+F, D+J, and E+K all have the same answer.
  4. The sums B+G and C+H are both even.
  5. C * E = J.

A B C D E
F G H J K

From Mensa Puzzle Calendar 2022 by Fraser Simpson, Workman Publishing, New York. Puzzle for January 6.

See The Solution Submitted by Charlie    
Rating: 5.0000 (2 votes)

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Solution soln | Comment 1 of 4
The completed 2x5 grid is as follows:
______________
|3_|7_|2_|1_|4_|        
|6_|9_|0_|8_|5 |

EXPLANATION:
The 3 simultaneous  cryptarithmetic equations: A*B=CD, B*C=DE, and C*E=J solves as:
(A,B,C,D,E,J)=(3,7,2,1,4,8) ..........(i)
Then, A+F=D+J=E+K, gives:
3+F=1+8=4+K
=> 3+F=4+K=9
=> F=6, K=5
Then, (G,H) (- (0,9) ......(ii)
By, the problem both B+G and C+H are even
Accordingly, from (i), we must have each of 7+G and 2+H  are even.
Then from (ii), we must have G=9 and H=0
Consequently,  the complete assignment  of values is as follows:
A=3, B=7, C=2, D=1, E=4, F=6, G=9, H=0, J=8, and K=5
The completed 2x5 grid has already been shown above.

*** Of course. this solution has been achieved with the aid of an online solver. Accordingly, this hardly constitutes an ANALYTIC SOLUTION, and I leave the task of resolving this puzzle analytically to someone else.

Edited on January 15, 2022, 7:34 am

Edited on January 15, 2022, 8:20 am
  Posted by K Sengupta on 2022-01-15 07:32:15

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