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# PSL4#15

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191
5 Answer: 6777

Aug 5, 2019

#1
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What are these questions?

Are you supposed to be solving them by hand within a reasonable amount of time?

It's pretty trivial solving them with software.

Thoughts?

Aug 6, 2019
#2
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a few lines of mathematica shows the smallest is 2666, and the largest is 9443

9443-2666 = 6777

Rom  Aug 6, 2019
edited by Rom  Aug 6, 2019
#3
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Actually, this is a written contest where you have to do 30 questions in 40 minutes by hand, no calculator.

dgfgrafgdfge111  Aug 6, 2019
#4
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432=  2*2*2*2*3*3*3*1   (times 1 as many times as you want)

So the single digit numbers that go into 432 are   1, 2, 3, 4, 6, 8, 9

To add 4 numbers to 20 I need an even number of even numbers.  ie, 0,2 or 4 even numbers

Lets see if i can split 432 into 4 odd single digit factors ...odd, odd, odd, odd      This is impossible.

Ok

Lets see if i can split 432 into 2 odd single digit factors and 2 even digit factors ...odd, odd, even, even

9 * 3 * 8 * 2  = 432       But these add to 22  So they are no good

9 * 3 * 4 * 4   = 432   These add to 20 9 * 1 * 8 * 6   = 432     But these add to 24 so they are no good.

3 * 3 * 6 * 8  = 432   These add to 20 AND LASTLY

Lets see if i can split 432 into 4 odd single digit factors ...even, even, even, even

6 * 6 * 6 * 2 = 432     These add to 20 So there are only 3 combinations of digits possible

9 * 3 * 4 * 4     This has the biggest digit so the largest number will be    9443

3 * 3 * 6 * 8

6 * 6 * 6 * 2     This has the smallest digit so the smallest number will be  2666

9443-2666 = 6777

Note: I did not use a calculator but I would not get many of this level question done in 40 minutes either.

Still not all the ones you have been asking have been so time consuming.

Aug 7, 2019
edited by Melody  Aug 7, 2019
edited by Melody  Aug 7, 2019
#5
+1

Thanks all of yyou!!!

dgfgrafgdfge111  Aug 7, 2019