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.
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.
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.
· 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. |