# Arithmetic Puzzle – Number Puzzle - make 21 using 17, 3, 3, and 1

Can you make 21 using 17, 3, 3, and 1 only using addition, subtraction, multiplication, and division?

Every number must be used only once in the calculations. Only the four operations listed above can be used.

### Comments for Arithmetic Puzzle – Number Puzzle - make 21 using 17, 3, 3, and 1

 Aug 08, 2012 Arithmetic Puzzle by: Staff Answer: Can you make 21 using 17, 3, 3, and 1 only using addition, subtraction, multiplication, and division? No you can’t make 21 using 17, 3, 3, and 1. Here’s why: The sum of all the numbers is 24 17 + 3 + 3 + 1 = 24 “If” the last step of the combination process is + or -: x + y = 24 (from above) x - y = 21 2x + 0 = 45 2x = 45 2x / 2 = 45 / 2 x * (2 / 2) = 45 / 2 x * (1) = 45 / 2 x = 45 / 2 x = 22.5 x + y = 24 22.5 + y = 24 22.5 - 22.5 + y = 24 - 22.5 0 + y = 24 - 22.5 y = 24 - 22.5 y = 1.5 So, if the last step is subtraction (or addition of a negative number) x = 22.5 y = 1.5 Now the question is: Is it possible to combine 17, 3, 3, and 1 to get 22.5 and 1.5? The answer is no. So the last step of the combination cannot be subtraction (or addition of a negative number). x + y = 24 (from above) x / y = 21 (x / y) * y = 21 * y x * (y / y) = 21 * y x * (1) = 21 * y x = 21 * y x = 21y x + y = 24 21y + y = 24 22y = 24 22y / 22 = 24 / 22 y * (22 / 22) = 24 / 22 y * (1) = 24 / 22 y = 24 / 22 y = 12 / 11, or 1.09091 x + y = 24 x + 12 / 11 = 24 x + 12 / 11 - 12 / 11 = 24 - 12 / 11 x + 0 = 24 - 12 / 11 x = 24 - 12 / 11 x = 264 / 11 - 12 / 11 x = (264 - 12) / 11 x = (252) / 11 x = 252 / 11, or 22.9091 x = 252 / 11, or 22.9091 y = 12 / 11, or 1.09091 Now the question is: Is it possible to combine 17, 3, 3, and 1 to get 252 / 11 and 12 / 11? The answer is no. Suppose the last step of the combination process is a multiplication (this will be similar to a division): x + y = 24 (from above) x / y = 21 x = sqrt(123)+12 y = 12-sqrt(123) Now the question is: Is it possible to combine 17, 3, 3, and 1 to get sqrt(123)+12 and 12-sqrt(123)? The answer is no. >>> the final answer: Since it is not possible to complete the “last step” of the combination process using addition, subtraction, multiplication, or division, then it is NOT POSSIBLE to combine 17, 3, 3, and 1 using only these four operations to get 21. Thanks for writing. Staff www.solving-math-problems.com