1-2-3-4 puzzle problem

Problem Statement

This problem is to make expressions for the numbers 1-25 using only the numbers 1-2-3-4 with the following rules:

  1. Your expression has to use each number once and cannot use each number more than once.
  2. You can only use the following operations: Division, Multiplication, Addition, Subtraction, Square root, Brackets and Factorial.
  3. You can use exponents 1-2-3-4 but it counts as one of your numbers. For example, one squared would count as using one and two.
  4. You can put 2 of your numbers together to make a 2 digit number. For example, 12 would count as using one and two, but you couldn’t make 10 this way seeing as how you don’t have 0.

Expressions and Process

To solve this problem and get what I got above, I started out trying different expressions in numerical order. When I got a number I wasn’t looking for at the time I moved it to a number I did need. A few tricks that I found worked really well were: saving the one on prime numbers to use it for addition or subtraction, throwing away the one by using it for multiplication and throwing away numbers by putting them as an exponent on one because one times itself is always one. When I got stuck I moved to a different number I needed, but if I was really stuck I traded an expression I had for one Ethan had.


Overall this was a fun challenge and I learned how to use different operations in combination with others to get passed restrictions like you have to use 1-2-3-4  once each. I found this slightly challenging and might want to try something a little more difficult. This problem reminds me of a game we played in 6th grade with my math teacher where we were given ordered numbers and had to find what operations to put between them. We played this game in teams and the challenge was to get it before the other team.

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