The ten digits 0 through 9 are to be placed in the grid below so that:
- The product of A and B is the 2-digit number CD.
- The product of B and C is the 2-digit number DE.
- The three sums A+F, D+J, and E+K all have the same answer.
- The sums B+G and C+H are both even.
- C * E = J.
From Mensa Puzzle Calendar 2022 by Fraser Simpson, Workman Publishing, New York. Puzzle for January 6.
1) C*E = J has only four solutions, because the digits must be distinct
Either
C E J
2 3 6
3 2 6
2 4 8
4 2 8
2) Then consider B*C = DE
The only possibilities are
BCDEJ
2 36 No possible value of B
43126
72148
34128
3) Then consider A*B = CD
Only possibility is
ABCDEJ
43216 No possible value of A
372148
34128 No possible value of A
4) Solution then proceeds as outlined by K Sengupta
Edited on January 15, 2022, 10:09 pm
Analytic Solution
