Reader Joe Antognini sent this in: Brazilian mathematician Inder Taneja has found a way to render every number from 1 to 11,111 by starting with either of these strings:

1 2 3 4 5 6 7 8 9

9 8 7 6 5 4 3 2 1

and applying any of the operations addition, subtraction, multiplication, division, and exponentiation. Brackets are permitted. For example:

6439 = 1 + 2 × (3⁴ × 5 × 6 + 789)

and

6439 = 9 × (8 + 7 + 6) + 5⁴ × (3² + 1)

Intriguingly, there’s one hole: There doesn’t seem to be a way to render 10958 from the increasing sequence.

Taneja’s paper is here. (Thanks, Joe.)

01/29/2017 UPDATE: Taneja tells me that, while it can’t be calculated using only basic operations, 10958 can be reached using factorials or square roots. Here are two factorials:

10958 = 1 + 2 + 3!! + (-4 + 5! + 6 – 7) × 89

10958 = 1 × 2 × (3!! – 4! × (5 + 6) + 7! – 8 – 9)