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Consider the sum: ABC + DEF + GHI = JJJ
If different letters represent different digits, and there
are no leading zeros, what does J represent?
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Answer / guest
The value of J must be 9.
Since there are no leading zeros, J must be 7, 8, or 9. (JJJ
= ABC + DEF + GHI = 14? + 25? + 36? = 7??)
Now, the remainder left after dividing any number by 9 is
the same as the remainder left after dividing the sum of the
digits of that number by 9. Also, note that 0 + 1 + ... + 9
has a remainder of 0 after dividing by 9 and JJJ has a
remainder of 0, 3, or 6.
The number 9 is the only number from 7, 8 and 9 that leaves
a remainder of 0, 3, or 6 if you remove it from the sum 0 +
1 + ... + 9. Hence, it follows that J must be 9.
| Is This Answer Correct ? | 6 Yes | 3 No |
Answer / nell
I agree that J represents 9. ABC, DEF, and GHI would
therefore be represented by 140, 273, and 586. However,
there is not enough information to identify which set of
letters represents which 3-digit number.
| Is This Answer Correct ? | 3 Yes | 4 No |
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