# How to make 18 from 1, 3, 4, 8

This question was on my sister's 5th-grade homework, practicing order of operations. It was to make 18, using the numbers 1, 3, 4, 8 and the operations +, -, and *. The instructions imply using each operation only once. Additionally, grouping with parenthesis is allowed.

Neither my sister, my father, or I were able to find a solution. I even tried writing a python script to attempt all possible solutions to the problem, to no avail.

Can you do what we can't? Or is the problem flawed?

Edit: Here is a picture of the original worksheet. The problem in question is #11. I assume that operations are only allowed once, because some of the other problems have an operation repeated, and because it refers to rearranging operations and numbers on a mat.

• Welcome to Puzzling.SE! I have a few questions - 1. Can the order of the numbers be changed? 2. Did you omit division on purpose or by accident? 3. Are there any other allowed operators (concatenation, exponents, roots, etc. – Brandon_J Mar 18 at 22:18
• @Brandon_J, Order of numbers can be changed. Division and other operations intentionally omitted. – BillThePlatypus Mar 18 at 23:18
• @ferret I've updated the question with the original worksheet. – BillThePlatypus Mar 18 at 23:18
• I suspect that the teacher either meant 16 or 17, as both are possible. – Brandon_J Mar 19 at 2:02
• I just added an answer. It was, in fact, a typo. – BillThePlatypus Mar 22 at 14:26

## 2 Answers

Here it is.....

$$18 * (4-3) = 18$$

• This works if concatenation is allowed. Considering it's a question for 5th graders, I doubt there is a "trick" like this, so I'm thinking it's a mistake by the teacher – ferret Mar 18 at 23:25
• I agree with ferret. It is highly unlikely that concatenation is allowed, given the circumstances. – Brandon_J Mar 19 at 2:04
• See, for example, problems five, six, and nine. If concatenation were allowed, there would be no need to join the digits of the 2-digit numbers together. – Brandon_J Mar 19 at 2:36
• @Brandon_J and ferret, you are both probably right. Let's wait for the teacher's explanation :-) – ppgdev Mar 19 at 2:52
• Yeah. Feel kinda bad for the teacher, tbh - I'm sure she'll feel bad for all the people that spent so much time on this. – Brandon_J Mar 19 at 3:02

As I had suspected, the teacher confirmed that the question was incorrect, and there is no correct answer. Thank you all for the attempts.