MIT Year Problem

MIT Technology Review has a Puzzle Corner column hosted by Allan Gottlieb. Every January the first problem posed is the so-called "Year" problem. Here's this year's problem:

Y2014. How many integers from 1 to 100 can you form using the digits 2, 0, 1, and 4 exactly once each; the operators +, -, × (multiplication), and / (division>; and exponentiation? We seek solutions containing the minimum number of operators; among solutions having a given number of operators, those using the digits in the order 2, 0, 1, 4 are preferred. Parentheses may be used for grouping; they do not count as operators. A leading minus sign, however, does count as an operator.

It turns out that it doesn't take very long to try every possible combination of operators and numbers and come up with the best solution. Enter a year in the text box below and click "Solve". Click here for a demo

Note: You can also enter a two or three digit number and get solutions for that number as well.

When comparing solutions the app applies two more rules to get the "best" solution:

• Pick the solution with the fewest parentheses.
• Pick the solution with simpler operators - avoid using minus and divide.