Operator Game Rules

Operator Game is a fun and creative way to play with numbers. The goal of the Operator Game is to create an equation to reach the target number from 4 given numbers using a set of allowed operators.

Rules: 

Operators allowed and points:

·       1 point: addition (+), subtraction (-).

·       2 points: multiplication (*), division (/).

·       3 points: exponent (2^3 or exp(2,3)), square root (sqrt(4))

Requirements: Each given number is used exactly once. No other numbers can be used. The same operator cannot be applied repeatedly if the result is the same or infinitely to get a converging number to avoid infinite points.

Goal: Find an expression with as many points as possible, using the given 4 numbers exactly once and the allowed operators to produce the target number.


Examples:

Numbers given are 2,3,4,5. Target number: 7

Possible solutions:

  • Expression A: 5+((2+4)/3) = 7. Operators used: +, +, /. Total poins: 1,1,2 => 4
  • Expression B: 3+5-(sqrt(4)/2) = 7. Operators used: +,-,sqrt, /. Total points: 1,1,3,2 => 7
  • Expression C: 3+5-sqrt(sqrt(4)/2)) = 7. Operators used: +,-,sqrt,sqrt,/. Total points: 1,1,3,3,2 => 10
  • Expression D: 3+5-sqrt(sqrt(sqrt(sqrt(4)/2)))) = 7. => Illegal expression since sqrt() was repeatedly applied to 1.
  • Expression E: Exp(5 + sqrt(4),sqrt(3-2)) = 7. => 12 points.

Tips on the Operator Game:

·        Square Root: sqrt(4) = 2 because 4 = 2*2. Sqrt(9) = 3. Sqrt(100) = 10.

·        Exponent: 2^3 = 2 * 2 * 2. 5^2 = 5 * 5 = 25.

·        Factorial: 3! = 3 * 2 * 1. 8! = 8 * 7 * 6 * 5 * 4 * 3 * 2* 1.

Example 1:

Numbers given are 2,3,4,5. Target number: 7

Expression A: 5+((2+4)/3) = 7. Operators used: +, +, /. Total poins: 1,1,2 => 4

Expression B: 3+5-(sqrt(4)/2) = 7. Operators used: +,-,sqrt, /. Total points: 1,1,3,2 => 7

Expression C: 3+5-sqrt(sqrt(4)/2)) = 7. Operators used: +,-,sqrt,sqrt,/. Total points: 1,1,3,3,2 => 10

Expression D: 3+5-sqrt(sqrt(sqrt(sqrt(4)/2)))) = 7. => Illegal expression since sqrt() was repeatedly applied to 1.

Expression F: Exp(5 + sqrt(4),sqrt(3-2)) = 7. => 12 points.

Other ways to make 7:

2^3 – sqrt((5-4)) = 7. => 8 points.

2*3+sqrt(5-4)=7. => 6 points

3*(2*sqrt(4))-5 => 8 poins.

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