NPR Sunday Puzzle (Oct 16, 2016): Five, Four, Three, Two, One, Blast-off!:
Q: This is a two-week challenge. Take the digits 5, 4, 3, 2 and 1, in that order. Using those digits and the four arithmetic signs — plus, minus, times and divided by — you can get 1 with the sequence 5 - 4 + 3 - 2 - 1. You can get 2 with the sequence (5 - 4 + 3 - 2) x 1.
The question is ... how many numbers from 1 to 40 can you get using the digits 5, 4, 3, 2, and 1 in that order along with the four arithmetic signs?
You can group digits with parentheses, as in the example. There are no tricks to this, though. It's a straightforward puzzle. How many numbers from 1 to 40 can you get — and, specifically, what number or numbers can you not get? Will Shortz will reveal his solution in two weeks.
Enjoy the two-week math challenge. Feel free to post *how many* numbers you can create, but just not specifics on which ones and with what expressions.
Edit: A bit of a trick here. You can create 39 numbers, but not 39. :)
A: Without resorting to tricks, you can write expressions for all but number 39.