Puzzle of the Day : 41
Equal Products
Each of the seven digits from 0, 1 , 2 ,3 4, 5, 6, 7, 8 and 9 is :
[1] Represented by a different letter in the figure above.
[2] Positioned in the figure above so that A × B × C, B×G ×E ,
and D × E × F are equal.
Which digit does G represent ?
From [1] and [2]: No letter can be 0,5,or 7. The product for each row, then, is a multiple of 1, 2, 3, 4, 6, 8, and 9. So the smallest possible product 8 ×9 or 72 and the product is a multiple of 72. But the product cannot be any of 72 × 3 , 72 × 2, etc. because it is not possible to get a product larger than 72 three times. So the product is 72.
Then:
72 = 1 × 8 × 9 = 2 × 36 = 2 × 4 × 9 = 3 × 24 = 3 × 4 × 6
Because 4 and 9 are used twice, B or E is 4 and the other is 9. So G is 2.
A possible arrangements of digits is:
6 8
4 2 9
3 1
2