Figures for letters

Logic Level 3

Professor Rackbrane the other morning gave his young friends this rather difficult problem. He wrote down the letters of the alphabet in this order:

ABCD X EFGHI = ACGEFHIBD

Every letter, he said, stood for a different digit, I to 9 (0 excluded). The number represented by the first four digits, when multiplied by the number containing five digits, equals the number containing all the nine digits in the order shown. Can you substitute digits for letters so that it works?

Give the answer as ACGEFHIBD in numerical format.


The answer is 642987153.

Syed Hamza Khalid by Syed Hamza Khalid , 17, France

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1 solution

This is the only thing that works. I don't think there is any mathematical method other than trial and error !

A ⇒ ⁣ 6 , B ⇒ ⁣ 5 , C ⇒ ⁣ 4 , D ⇒ ⁣ 3 , E ⇒ ⁣ 9 , F ⇒ ⁣ 8 G ⇒ ⁣ 2 , H ⇒ ⁣ 7 , I ⇒ ⁣ 1 \large A\Rightarrow \!\,6,\ B\Rightarrow \!\,5, \ C\Rightarrow \!\,4, \ D\Rightarrow \!\,3, \ E\Rightarrow \!\,9, \ F\Rightarrow \!\,8\, \ G\Rightarrow \!\,2, \ H\Rightarrow \!\,7, \ I\Rightarrow \!\,1

Therefore,

A B C D × E F G H I = A C G E F H I B D \large ABCD \times EFGHI = ACGEFHIBD

6 , 543 × 98 , 271 = 642 , 987 , 153 \large 6,543 \times 98,271 = 642,987,153

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