# Using 20, 17, 16, 8, 7 to make 9

You can use $$+, -, \times,$$ or $$/$$ (namely $$\div$$).

Use all five numbers (20, 17, 16, 8, and 7) only once to make $$9$$.

From what I've been told there are $$4$$ answers. The only one I've been able to figure out is:

$$\Bigg((17-7)\times\left(\frac{20}{8}\right)\Bigg)-16=9$$

Any help would be appreciated.

• Are the given numbers supposed to be used only once ? Oct 2, 2018 at 1:03
• is concatenation allowed? Oct 2, 2018 at 4:11
• You can only use them once. I don't know what concatenation is but I would assume no. I was told addition, subtraction, multiplication, and division. Oct 2, 2018 at 14:43
• Nice. I've been working on this thing for weeks. Oct 3, 2018 at 19:07

Here is one:

$$\Bigg((20-7)\times\left(\frac{16}{8}\right)\Bigg)-17=9$$

1. $$20\times\frac{17-7}{8}-16$$

2. $$\frac{20\times(16-8)-7}{17}$$

3. $$(20-7)\times\frac{16}{8}-17$$

4. $$167+20-178$$

• $1$ and $3$ are the same equation Oct 2, 2018 at 5:40
• @ShahriarMahmudSajid fixed it.
– Oray
Oct 2, 2018 at 5:40
• not sure if concatenation is allowed, asked the OP, didn't get an answer yet. Oct 2, 2018 at 5:49
• Concatenation is not allowed. Oct 4, 2018 at 13:16
• @NateSmith these are only solutions, I did it with computer, checked all solutions. so if concatenation is not allowed, there are 3 answers.
– Oray
Oct 4, 2018 at 13:17