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.
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
soln
