Find the smallest number comprised of only 3’s and 7’s which fits the following conditions:

1) It has at least one 3;
2) It has at least one 7;
3) It is divisible by 3;
4) It is divisible by 7;
5) The sum of its digits is divisible by 3;
6) The sum of its digits is divisible by 7.

(In reply to the computer doing the trial and error by Charlie)

Close but no cigar...

 

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How to solve

3*7  = 21  but no number of figures of 7's and 3's solve it

so 21*2 = 42, so how many 3's and 7's can make 42 and devive by 7's and 3's  (i.e.  21 + 21)

so 7 3's and 3 7's

 

Make an order and the last digit MUST be 3.

3333337773 added totals 42

/3 = 1111112591

/7 = 476191110

 

Took about 1 hour with pen and paper.

 

Posted by stewart on 2006-04-10 07:23:03