Each letter in the grid represents a different digit from 1 through 9. What is each, given that
- A is smaller than B and A*B is a 2-digit number in which the second digit is two more than the first.
- One of the rows contains three consecutive digits, not necessarily in order.
- D+E = F
- E^2 = G
- H = 7
From Mensa Puzzle Calendar 2018 by Fraser Simpson, Workman Publishing, New York. Puzzle for December 11.
(In reply to
Answer by K Sengupta)
The simultaneous cryptarithmetic equations:
A+2=B, D+E=F, E^2=G, H=7 solve as:
A B D E F G H
1 3 6 2 8 4 7
2 4 5 3 8 9 7
3 5 6 2 8 4 7
4 6 2 3 5 9 7
4 6 5 3 8 9 7
6 8 1 2 3 4 7
6 8 1 3 4 9 7
6 8 2 3 5 9 7
6 8 3 2 5 4 7
Case 1: A, B C are consecutive in any order.
All the nine rows lead to a cryptarithmetic contradiction in some form or another.
Case 2-: D, E, and F are consecutive in any order.
We observe that D=1, E=2, F=3 in the 6th row. . Therefore, (8,6,1,2,3,4,7) is a solution. But, then C can assume any of the two unassigned values: 5 or 9. This is a contradiction.
Cae 3: G, H, and I are consecutive in any order.
From row 7, we observe that:
ABDEFGH
4623597
so the middle digit 8 is unassigned. So, for I=8 ,we have G, H and I as consecutive in an arbitrary order.
Our assignment is now:
ABDEFGHI
46235978
The only unassigned digit is 1 which is assigned to the lone unassigned letter, that is, C.
Consequently our required solution is now as follows:
4 6 1
2 3 5
9 7 8
****************** Quod Erat Demonstrandum *******************
Edited on April 7, 2022, 9:24 pm
Explanation to Puzzle Answer
