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2-Row Number Grid (Posted on 2022-01-15)

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.

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.

Submitted by Charlie

Rating: 5.0000 (2 votes)

Solution: (Hide)

Since C * E = J, C and E can be only 2 and 3 or 2 and 4, not necessarily respectively, as zero or 1 would lead to a repetition of either zero or the other multiplicand for the 1.
The values of A and B determine the remainder of the top row. The only values of A and B that lead to consistent values for CD and DE (the same value for D), and no repetitions are 37, 54 and 67. The lead respectively to top row being 37214, 54208, and 67428.
But we know that E can be only 2, 3 or 4, so the top row must be 37214.
Only 9 works as the common sum of A+F, D+J and E+K, and the bottom row as 69085.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: Answer	hoadao3493	2022-06-01 13:21:44
Answer	Math Man	2022-01-15 22:34:50
Analytic Solution	Steve Herman	2022-01-15 22:01:28
soln	K Sengupta	2022-01-15 07:32:15

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