Assistance with "Negative Countdown"

Question

I'm trying to help my sister with this maths question:

In "Negative Countdown" you can add or subtract all of the numbers given to make the target number. The numbers must be only used once, and all of the numbers must be used.

A) target = -5 numbers: -5, 9, 7

B) target = 2 numbers: 8, 7, 5, -4

C) target = -4 numbers: -4, -3, 7, -3, -6

I cannot get an answer for part C using all of the numbers. Parts A and B are fine.

Here is the working for part A and B

A) - 3 - 9 + 7 = -5

B) - 4 - 7 + 5 + 8 = 2

Here is my attempt for C:

• 3 - 3 = 0 -7 - 3 = -10
• 10 - (- 6) = -4

However this is wrong as I have used -3 twice and have not used 6.

I am really stuck and we cannot get the answer out. I believe the book is wrong, but I am not sure. Can anyone give me some suggestions on what to do?

This is UK year 7 maths, and even though I have done A-Level maths, I obviously cannot use calculus and difficult algebra to explain this to her.

Sorry for the incorrect tags. I cannot think of any appropriate tags for this. Thanks for any advice :)

Answer 1

There is no way to answer the question under the given constraints:

• The target number ($-4$) is even
• Any result of adding/subtracting $\{-4,-3,7,-3,-6\}$ is odd