NPR Sunday Puzzle (Jan 4, 2026): Equation of the YearQ: This week's challenge is a numerical one. Take the nine digits -- 1, 2, 3, 4, 5, 6, 7, 8, 9. You can group some of them and add arithmetic operations to get 2011 like this: 1 + 23 ÷ 4 x 5 x 67 - 8 + 9. If you do these operations in order from left to right, you get 2011. Well, 2011 was 15 years ago. Can you group some of the digits and add arithmetic symbols in a different way to make 2026? The digits from 1 to 9 need to stay in that order. Will knows of two different solutions, but you need to find only one of them.
I'm a little annoyed that the example doesn't follow the order of operations and instead must be performed left to right. It would have to be (1 + 23) ÷ 4 x 5 x 67 - 8 + 9 to work correctly in most calculators.
I have one expression that works either way, three expressions that work left to right and one that only works using the standard order of operations. I have a feeling that Ed Pegg Jr. provided the two that work using the standard order of operations.
My only hint is 390,625.
Edit: To "brute force" this, you could take the digits 1 to 9. Then you have 5 choices of symbol (nothing, or one of the basic operators) to put in the 8 spaces between each digit. That results in 5^8 or 390,625 strings that would need to be evaluated. I submitted the first answer below because it has all the multiplication first so going left to right is the same as following the standard order of operations.
Note: The two answers following PEMDAS order are the ones that Ed Pegg Jr. provided in his
Wolfram Community post which makes me think the PEMDAS answers are what were originally given to Will. I've contacted Will to see if that's the case and if Will introduced the non-standard "left to right" example and wording. I'll let you know if I hear back.
A: 12 x 34 x 5 - 6 - 7 + 8 - 9 = 2026 | PEMDAS or L to R
(1 + 2) x 3 x 4 x 56 - 7 + 8 + 9 = 2026 | L to R
(1 x 2 + 34) x 56 - 7 + 8 + 9 = 2026 | L to R
(12 - 3) x 4 x 56 - 7 + 8 + 9 = 2026 | L to R
1 + 2 + 345 x 6 - 7 x 8 + 9 = 2026 | PEMDAS
Note: As suspected, the intended solutions followed PEMDAS without parentheses and the whole "left to right" example was a confusing red herring introduced by Will