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Math Magic Archive

Problem of the Month (July 2015)

Using the positive integers from 1 to n each used exactly once, along with any number of the 4 arithmetic symbols (+, – ×, ÷) and parentheses, what is the equation you can make with the largest number on both sides? What is the largest number a(n,k) that can be represented if there are k equal expressions, which together use the numbers 1 through n exactly once? How fast do these numbers grow? Is it true that a(n,k)k / n! → 1 as n → ∞?


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