PSL4#15

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?

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.