Six Digits

Number Theory Level pending

If a six digit number a b c d e abcde 8 (where each letter is a digit) is divided by 2, a new six digit number is obtained as 2 a b c d e abcde . Find the sum of digits of the original six digit number a b c d e abcde 8.


The answer is 48.

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1 solution

The only way for this to work is if a a is equal to either 4 or 5. But we can disprove the latter because the least 2 a b c d e abcde could be is 250000 and 250000 x 2 is not equal to 500008. Thus, the only number that satisfies 2 a b c d e abcde is the number directly below 250000 which is 249999 and 249999 x 2 = 499998 . 4 + 9 + 9 + 9 + 9 + 8 = 48 \boxed{48} .

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