# A Simple Math Puzzle

So my last math puzzle was too easy apparently, and this one might be too. Either way, the rules are the same.

• No rotation.
• No duplication.
• No combination.
• No rounding.
• No computers.

## Good luck to all of you!

You are given the following set of numbers: $$1, 2, 3, 5, 6, 9$$. Inject these numbers into the following equation to create a true statement.

$$\frac{21a + \frac{5b}{c}}{d} + e = f$$

## Note

It was pointed out in the chat that I made a typo. I've corrected the number set; and I apologize to everyone for that mistake.

• Oh boy, 720 possible combinations to choose from... Where to start..... – Cubemaster Sep 21 at 19:14
• Is there a single solution? – Weather Vane Sep 21 at 19:16
• There is only one solution. – PerpetualJ Sep 21 at 19:19
• You sure there is a solution to this? – Robert S. Sep 21 at 19:23
• After trying to solve this, I gave up and made a Python script to try every possible combination. I haven't been able to find an answer that doesn't require rounding. I'll check again in case I made a mistake, but it's either that or this requires some lateral thinking. – Racso Sep 21 at 19:55

$$\frac{21a + \frac{5b}{c}}{d} + e = f$$ is true when

a = 2
b = 3
c = 5
d = 9
e = 1
f = 6

• HAHA That was an awesome loop hole; however, it isn't the correct answer. I've updated the post as I made a typo. That should help lol – PerpetualJ Sep 21 at 20:13
• @Perp Changed now that the 4 is a 6 – PotatoLatte Sep 21 at 20:14

Also not really an answer, but this is the closest I've gotten

$$\frac{21*1 + \frac{5*4}{3}}{9} + 2 = 5\tfrac{2}{27}$$ which is only off by $$\frac{2}{27}$$. So far that's the smallest margin of error that I could find. However rounding isn't allowed so...

$$\frac{21*2 + \frac{5*3}{5}}{9} + 1 = 6$$

• The answer is similar to this. :) – PerpetualJ Sep 21 at 19:48
• @Perp Is mine correct? – PotatoLatte Sep 21 at 20:05
• Dang it! Too slow again! :P – Luke C. J. Currie Sep 21 at 20:22
• d=9 is an overlap. also f=6 is kinda close to f = 5 and 2/27... – Luke C. J. Currie Sep 21 at 20:33
• He found $d$ and $f$ was close but no rounding allowed. – PerpetualJ Sep 21 at 20:34

Not an answer, but some facts I have found to help the community:

C != 4,9

• That is a true statement. :) – PerpetualJ Sep 21 at 19:47