# A puzzle and a call for help.

• Aug 17th 2009, 05:28 PM
bruxism
A puzzle and a call for help.
Hi everyone.

This is a puzzle that has been given to one of my tutoring students as an assignment. I'm supposed to help him out with it today and I'd like to know all the answers before I see him. Problem is I'm missing a few answers. Anyone like to pitch in?

Using 4 6's and operations (+-*/()) can you make calculations that add up to all the number from 1 - 9. Here are some examples.

66/66 = 1
6/6 +6/6 = 2
.
.
.
.
6/.6 - 6/6 = 9

And now, can you also do the same for 4 7's, 4 8's and 4 9's.

I've got most of them out but i'm just stuck on a couple. I'd really appreciate if someone could work out and send, either in this thread or via PM's the answers to the following.....

6's = 8
7's = 4
8's = 4 & 5
9's = 4, 5 & 6

• Aug 17th 2009, 07:24 PM
artvandalay11
$\frac{6+6}{6}+6=2+6=8$

$\frac{77}{7}-7=11-7=4$

$\frac{8*8}{8+8}=\frac{64}{16}=4$

please post the other answers if you get them, this is pretty annoying
• Aug 17th 2009, 09:01 PM
bruxism
Quote:

Originally Posted by artvandalay11
please post the other answers if you get them, this is pretty annoying

You think you're annoyed, I've been puzzling over this for ages and it's doing my head in. I hope there is an answer and this kids teacher isn't just trying to be funny.

I worked out a couple using square roots, but they weren't suggested as operations in the original question.
• Aug 17th 2009, 09:25 PM
VonNemo19
$\frac{9+9}{9}+\frac{9+9}{9}=4$

$\frac{9+9}{9}+\frac{9+9}{9}+\frac{9+9}{9}=6$

$\frac{9+9+9}{9}+\frac{9+9}{9}=5$

This is a great excercise. It trains one to recognize different ways to rewrite. It also develps one's ability to recognize patterns.
• Aug 17th 2009, 09:45 PM
bruxism
i agree it's a great exercise but unfortunately you can only use 4 nines in your answers, not 6 9 and 7 as you have in your answers.
• Aug 17th 2009, 09:50 PM
VonNemo19
Quote:

Originally Posted by bruxism
i agree it's a great exercise but unfortunately you can only use 4 nines in your answers, not 6 9 and 7 as you have in your answers.

Well, in that case, you're out of luck.
• Aug 17th 2009, 09:58 PM
Wilmer
The 9's for 4,5,6 looks impossible....unless you cheat a bit...

9/sqrt(9) + 9/9 = 4

sqrt(9) + sqrt(9) - 9/9 = 5

(9-9) / 9 + 9 turned upside down = 6 (Clapping)
• Aug 18th 2009, 02:30 AM
bruxism
just got back from tutoring. The kid told me the teacher has added square roots to the list of allowable operations.

Wish he had of put that in the original assignment sheet though, would have saved me lots of this(Headbang)

thanks heaps for the help
• Aug 18th 2009, 05:00 AM
Soroban
I used a general digit $x$ and came up with these . . .

. . $\begin{array}{ccc}\dfrac{x}{x}\cdot\dfrac{x}{x} &=&1 \\ \\[-2mm]

\dfrac{x}{x} + \dfrac{x}{x} &=& 2 \\ \\[-2mm]

\dfrac{x+x+x}{x} &=& 3 \\ \\[-2mm]

\vdots & & \vdots \end{array}$

. . $\begin{array}{ccc}
x - \dfrac{x+x}{x} &=& x-2 \\ \\[-2mm]

\dfrac{x\cdot x - x}{x} &=&x-1 \\ \\[-2mm]

\vdots & & \vdots \\ \\[-2mm]

\dfrac{x\cdot x + x}{x} &=& x+1 \\ \\[-2mm]

x + \dfrac{x+x}{x} &=& x+2

\end{array}$

• Aug 18th 2009, 06:13 AM
Wilmer
Sqrt(8 + 8) + 8/8 = 5
• Aug 22nd 2009, 11:15 PM
Bruno J.
I don't understand why a teacher would ever give such a problem to solve.

1. The only way to solve it is by trial and error;
2. The solution brings no insight whatsoever about anything.

No wonder so many kids hate "math".
• Aug 23rd 2009, 02:02 AM
Opalg
Quote:

Originally Posted by Bruno J.
I don't understand why a teacher would ever give such a problem to solve.

1. The only way to solve it is by trial and error;
2. The solution brings no insight whatsoever about anything.

No wonder so many kids hate "math".

I completely disagree. There are certainly too many kids who "hate math", but there are many who relish the challenge of tackling puzzles like this, which stimulate their mathematical imagination and creativity.
• Aug 23rd 2009, 04:15 AM
Wilmer
Agree with you 100% Opal.

James F Fixx: "Puzzles are to the mental what jogging is to the physical".
• Aug 23rd 2009, 06:47 AM
Bruno J.
Quote:

Originally Posted by Opalg
I completely disagree. There are certainly too many kids who "hate math", but there are many who relish the challenge of tackling puzzles like this, which stimulate their mathematical imagination and creativity.

I fully agree with everything you have said except the words "like this". I'm all for puzzles but I fail to see how this particular one, for which blind trial and error is the only way, could stimulate creativity. In my opinion it risks dulling it just as much. This problem has nothing to do with mathematical reasoning.

The only thing I could see this as being useful for is getting better with the "priority of operations".
• Aug 23rd 2009, 07:39 PM
Wilmer