Brain Teasers
Threes and Sevens 2
Which is the smallest natural number that satisfies the following conditions:
(1) Its digits consist of, and only of 3's and 7's.
(2) Its digital sum is divisible by 3 and 7.
(3) The number itself is divisible by 3 and 7.
(1) Its digits consist of, and only of 3's and 7's.
(2) Its digital sum is divisible by 3 and 7.
(3) The number itself is divisible by 3 and 7.
Hint
It's not very hard.Answer
From conditions 1 and 2, we know that we need at least 3 7's and 7 3's.Their sum is divisible by 3, therefore any number they make is divisible by 3.
By trial and error, we see that none of 3333333777, 3333337377, 3333337737, 3333337773, 3333373377, 3333373737, 3333373773, 3333377337 and 3333377373 is divisible by 7.
3333377733 is divisible by 7 (the quotient is 476196819.)
Therefore, the number we're looking for is 3333377733.
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