Math Is Fun Forum

davidtrinh

Member

Registered: 2016-12-03

Posts: 10

I don''t understand the steps in this solution.

Hi everyone. I am a new member. I am happy to be part of the forum. Someone solved this problem for me, but I don't understand the steps. I am going to write it down below.

(ex) Determine the sum of all the 3-digit numbers that can be made by choosing 3 different numbers from the list 1, 2, 3, 4, 5, 6, 7.

This is his solution. 30(1+2+3+4+5+6+7) + 300(1+2+3+4+5+6+7) + 3000(1+2+3+4+5+6+7) = (30+300+3000)(28) = 93240.

I have two questions about the solution.

(1) Where do the numbers 30, 300 and 3000 come from?

(2) Why do you have to add up all the whole numbers from 1 to 7?

Could someone please explain the steps to me? Thanks a lot.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: I don''t understand the steps in this solution.

Hi;

There are 7 x 6 x 5 = 210 total ways to arrange the numbers 1 to 7 in groups of 3. So in the ones digit there will be 30 ones, 30 twos, 30 threes etc. He just adds up all the numbers in the first column which will be 30(1+2+3+4+5+6+7). Is it clear now?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

davidtrinh

Member

Registered: 2016-12-03

Posts: 10

Re: I don''t understand the steps in this solution.

Yes, I now see why there are 30 ones, 30 twos, .... in the ones digit. Shouldn't there be 30 ones, 30 twos, ... in the tens digit as well? Why are there 300 of each in the tens digit?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: I don''t understand the steps in this solution.

There are 30 of each in the tens place but each of them is multiplied by 10 because a 5 in the tens place is 50. He could just as easily said 30(10+20+30+40+50+60+70).

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.