# Replace in number 54 *** asterisks various odd with figures so that the received number was divided into 15. How many various numbers can it will turn out? Prove the answer.

Augra

76

..............5.415, 5.475esli the condition that figures have to be odd, possible only two options is obligatory: 5415 and 5475. The criterion for divisibility on 15 consists of two ave. of signs: On 3 and on 5. Therefore, if the number comes to an end on 0 or 5 and the sum of its figures is divided into 3, then the number will be divided into 15. Simple selection we come to the answer. And in principle such options are possible: 5430, 5460, 5490, 5445, 5415, 5475. But zero is an even number. Therefore only 5415 and 5475 will be responsible

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