Properly plussed

Where should there be + signs be in digits 123456789 to add to a total of 99? And where in 1234567 to add to a total of 100?

Reveal solution

There are a lot of options, so we need to try to narrow them down. If we have plus signs between all numbers we get 1+2+3+4+5+6+7+9 = 45. To change the last digit of this sum from 5 to 9–as we need to get 99–there needs to be six less in the sum. We can do this by removing plus sign and promoting digits to the tens column. The two ways to get six fro...