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How many 4 digit numbers have the property that the last digit is at least 4 times the first digit?

 Feb 28, 2020
 #1
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If the first digit from the left is 1, then there are: 1  x  10  x  10  x  6 = 600 such numbers

If the first digit from the left is 2, yjen there are: 1  x  10  x  10  x  1 = 100 such numbers.

 

600 + 100 = 700 numbers in total

 Feb 28, 2020
 #2
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It's clear  that the first digit  must  either  be  a 1 or a 2

 

If the first digit is a 1 , we have 6 possibilities for the last digit  [4,5,6,7,8 or 9]

So  there  are  10 * 10 *  6   = 600   4-digit numbers  of this type

 

If the first digit  is  a 2, we have  2 possibilities for the last digit  [8  or  9]

So there  are 10 * 10 * 2  =  200     4-digts  of this type

 

So.....we  have   600 + 200  =  800    4-digit integers

 

cool cool cool

 Feb 28, 2020

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