All Ten Solver

The All Ten game is a mathematical puzzle whose objective is to use four numbers given only once each, combined with basic operations (+, –, ×, ÷) and possibly parentheses, to obtain all the numbers from 1 to 10.

The aim of the game is to find the 10 numbers from 1 to 10, using the 4 given digits.

— Use each number exactly once per calculation

— Allow only the following operations: addition (+), subtraction (–), multiplication (×), division (÷)

— Allow parentheses to change the order of operations

— Do not use exponents, roots, factorials, or concatenation

The easiest way to solve the 10 All Ten problems is to use the dCode solver. Enter the four numbers, and the solutions for numbers 1 through 10 will be calculated.

Alternatively, here are a few tips:

— Start with the smallest target numbers (1 and 2); they often have simpler solutions.

— Look for symmetries: if an expression yields N and ends with the addition of a small digit like 1 or 2, then the same calculation but with the subtraction of that small digit gives a different result.

— Avoid calculations with multiplications resulting in very large numbers, or with non-integer divisions; these rarely lead to a viable solution.

— With concatenation: allow the formation of two-digit numbers (e.g., 1 and 2 to write 12)

— With exponents: allow powers (e.g., 2^3 = 8)

— With factorials: use the ! notation (e.g., 4! = 24)

— With 5 or 6 numbers

— With more target numbers, why limit ourselves to 1 to 10 when 100 isn't that far off!