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Start with a three-digit number and repeat the digits to make a six-digit number, for instance 379379. Now divide by 7, then divide the answer by 11 and then divide this answer by 13.
What do you notice, does it always happen and what is the explanation?
Yes it does and we get initial number, see explanation below:
xyz xyz= xyz + xyz*1000= xyz*1001= xyz* 7*11*13 so when divided we get the initial three- digit number
 +  +  = 30
Fill the boxes using one of these numbers 1, 3, 5, 7, 9, 11, 13, 15
You can also repeat the numbers.
What is the number if it divides exactly by 13 and when you write its digits in reverse order you make a square number. (You get a square number when you multiply a number by itself - 64 is square because it is 8 times 8)
How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 0, which are divisible by 5 and none of the digits is repeated?
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