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1. How many three digit numbers are there such that the digits are non-zero, the tens digit is a multiple of the hundreds digit, the units digit is a multiple of the tens digit, and none of the digits are the same?

 

2. Find the number of positive integers \(n \le 1000\) such that \(15n\) is a perfect square.

 Nov 1, 2019
 #1
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1. The answer is 2*2*3 = 12.

 

2. The perfect squares from 1 to 1000 are 1, 4, 9, ..., 31^2.  There are only two numbers that are multiples of 15, so the answer is 2.

 Nov 1, 2019
 #2
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2 )  Here's what I get  for "n"

 

                        n

3 * 5   * 1   =   15

3 * 5  * 4  =     60

3 * 5 * 9   =   135

3 * 5 * 16  = 240

3 * 5 *  25  = 375

3 * 5  * 36  = 540

3 * 5 * 49 =  735

3 * 5 * 64 =  960

 

 

cool cool cool

 Nov 2, 2019
 #3
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1)  These are the only numbers that meet all the conditions:

 

124   126   128   136   139   148   248   Total =  7

 Nov 2, 2019

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