Here's one for Keltin

[miniman]

2 different ways. If you look at Keltin's examples - the remaining digits all add up to , you add whatever to get to 9.

198= 1+9+8=18= 1+8=9,
180= 1+8+0 = 9

etc.

 

[keltin]

What about what miniman's wife's answer? Is that right?

Lee

That would work, but you must account for a 0 return

Take 321 – 123 = 198

I circle the 9 and then type in 1 and 8

Then we subtract those 2 numbers from 9. So 9 – 8 = 1, and then 1 – 1 = 0.......but the number I picked was 9 and not 0?

But, since 0 is not allowed in this trick, we can say that if this operation results in a 0, then the number must have been 9. As in the case of 99 being the remainder --> 9 - 9 = 0, and the number we picked is 9.

Conversely, you simply add everything up and do a single subtraction.

321 – 123 = 198 and I pick the 8 leaving 1 and 9. Obviously, you can’t subtract the 9 and the 1 from 9 since that is a negative number. So, add the 1 and 9 together:

1 + 9 = 10.........1 + 0 = 1.

So we have 1 and 9 – 1 = 8 which is the number we picked.

Then for a 4 digit number, you do the same

7654 – 4765 = 2889

I pick 8 which leaves 289. So 9 – 9 = 0....and we still have the 2 and 8 to deal with which gives a negative number. Unless you say 2+8+9 = 19 = 1+9 = 10 = 1+0 = 1.

9 – 1 = 8.