A place I would like to share some concepts, ideas, puzzles that simulate the minds of those interested in Math - for competitions or fun.
Wednesday, December 14, 2011
Puzzle 14 - Divisibility by 99
Consider the digits 3, 4, 7, 8, 3, 5. Add one more digit to this list, without disturbing the order of appearance of existing digits, to make a seven digit number that is divisible by 99. Find all such numbers.
To be divisible by 99, the sum of the digits should be divisible by 9. So, the digit to be included is 6. Further, the number should be divisible by 11, we should see the combination of digits that can satisfy the criterion for divisibility by 11. The right combination is 3, 7, 3, 5 for odd places and 4, 8, 6 even places. So, there will be 12*6=72 numbers.
2 comments:
3478365
pavankrishna
To be divisible by 99, the sum of the digits should be divisible by 9. So, the digit to be included is 6. Further, the number should be divisible by 11, we should see the combination of digits that can satisfy the criterion for divisibility by 11. The right combination is 3, 7, 3, 5 for odd places and 4, 8, 6 even places. So, there will be 12*6=72 numbers.
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