Question

How many three-digit numbers have the first digit equal to the sum of the other two digits?

Answer 1

Answer:

54 is the answer

Step-by-step explanation:

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Answer 2

Answer:

Let the number be xyz

1) x is 9, so y+z=9

Ways : (9,0); (8,1);(7,2);(6,3);(5,4) ..

Each of the above 5 ways can be taken as 2 different arrangements.. 981 or 918

So 5*2=10

2) x is 8, so y+z=8

Ways : (8,0);(7,1);(6,2);(5,3);(4,4) ..

4 of the above 5 ways can be taken as 2 different arrangements..

So 4*2+1=9

3) x is 7, so y+z=7

Ways : (7,0);(6,1);(5,2);(4,3)

Each of the above 4 ways can be taken as 2 different arrangements..

So 4*2

4) x is 6, so y+z=6

Ways : (6,0);(5,1);(4,2);(3,3)....

3 of the above 4 ways can be taken as 2 different arrangements..

So 3*2+1=7

And so on

There is a pattern...

So 10+9+8+7+6+5+4+3+2=54

Last 2 is when x is 1...

101 or 110

So the answer is 54