Math Problem Statement

Using each of these numbers exactly once 5, 8, 12, and 6, create 13 mathematical expressions. Each expression should evaluate to the numbers 1 through 13.

Solution

Let's create mathematical expressions using the numbers 5, 8, 12, and 6 exactly once in each expression. The goal is to obtain the numbers 1 through 13 as the results of these expressions.

  1. 1285+2=112 - 8 - 5 + 2 = 1
  2. 6÷(128)+56=26 \div (12 - 8) + 5 - 6 = 2
  3. 128+6÷6=312 - 8 + 6 \div 6 = 3
  4. 58+12÷6=45 - 8 + 12 \div 6 = 4
  5. 128+65=512 - 8 + 6 - 5 = 5
  6. (128)×6÷12=6(12 - 8) \times 6 \div 12 = 6
  7. 812+5×2=78 - 12 + 5 \times 2 = 7
  8. 8+512+7=88 + 5 - 12 + 7 = 8
  9. 8+5(12÷6)=98 + 5 - (12 \div 6) = 9
  10. 1258+10=1012 - 5 - 8 + 10 = 10
  11. 125+4=1112 - 5 + 4 = 11
  12. (12×6)÷12+5=12(12 \times 6) \div 12 + 5 = 12
  13. (128)+(5×2)=13(12 - 8) + (5 \times 2) = 13

Would you like more details or explanations on how these expressions were formed? Here are 5 related questions for further practice:

  1. Can you create a different set of expressions that evaluates to the numbers 1 through 13 using the same four numbers?
  2. How would these expressions change if we added a fifth number to use in each expression?
  3. Can you find another set of four numbers that can produce all the values from 1 to 13?
  4. What happens if you restrict the operations allowed to only addition and subtraction?
  5. Could you form the numbers 14 through 20 with the same set of numbers?

Tip: Breaking down each target number into possible operations can simplify the process of creating these expressions.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Operations
Order of Operations
Number Theory

Formulas

Basic arithmetic operations

Theorems

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Suitable Grade Level

Grades 6-8