# Math puzzle help

#### dboxall123

##### New member
Hello everyone. I am trying to complete a programming challenge, of which I have taken a screenshot of and posted on flikr.

I was wondering if there was some math genius on here who could help me solve the puzzle. Forget about the programming part, I can do that. All I need is some advice on the math part of it. I have absolutely no idea how to even begin working out the value of each shape. I sat down with a pen, a piece of paper and a calculator to try and work something out, but my mind is absolutely blank. Any advice would be greatly appreciated.

Thanks,
Dan

ps: I apologise if I've put this in the wrong topic, but I have no idea what sort of method would be used to work something like this out.

#### MarkFL

Staff member
It appears to me that you have 10 linear equations in 5 unknowns. Do you have any experience solving linear systems of equations?

#### dboxall123

##### New member
Hi MarkFl, thanks for the reply. I do not have any experience in solving linear systems of equations. I'm going to try and learn about it now.

#### MarkFL

Staff member
Hi MarkFl, thanks for the reply. I do not have any experience in solving linear systems of equations. I'm going to try and learn about it now.
I would assign a different variable to each shape and then write down the sums represented by the rows and columns and then use substitution and elimination to obtain a solution.

#### dboxall123

##### New member
I would assign a different variable to each shape and then write down the sums represented by the rows and columns and then use substitution and elimination to obtain a solution.
That makes sense, thanks mate. If I do decide to go and learn about systems of linear equations and matrices, do you think that I am likely to learn a slightly more elegant solution? The answer needs to be submitted within 2 seconds, and the puzzle changes every time the page is refreshed. It may take me a while to learn (as you can probably tell, my maths is very rusty) but the challenge is not going anywhere.

#### MarkFL

Staff member
That makes sense, thanks mate. If I do decide to go and learn about systems of linear equations and matrices, do you think that I am likely to learn a slightly more elegant solution? The answer needs to be submitted within 2 seconds, and the puzzle changes every time the page is refreshed. It may take me a while to learn (as you can probably tell, my maths is very rusty) but the challenge is not going anywhere.
Unless I am missing something, 2 seconds is an extremely and unreasonably small amount of time to solve such a puzzle. I don't think I could even enter 5 values into text fields in that amount of time even if I were able to "see" the solution immediately.

#### dboxall123

##### New member
Unless I am missing something, 2 seconds is an extremely and unreasonably small amount of time to solve such a puzzle. I don't think I could even enter 5 values into text fields in that amount of time even if I were able to "see" the solution immediately.
You misunderstand the challenge mate, I have to write a computer program to grab the puzzle, solve it and then post back. Once my program is written, I will not have to type anything - it will grab the puzzle, solve it and then post it back automatically for me. All I was wondering is if learning about linear systems and matrices would enable me to write a more elegant solution to solve this problem. Once I've learnt how to solve it on paper, I can then begin to write a program to do all of the above for me

#### MarkFL

Staff member
...Once my program is written, I will not have to type anything - it will grab the puzzle, solve it and then post it back automatically for me...
Okay, that's what I was missing.

#### dboxall123

##### New member
So, if I learn about this stuff, will I (eventually) learn an equation that can I can use to solve this? I'm asking you to give me one, just wondering if it's going to be worth learning about. Is it even possible to solve this in any way other than substitution and elimination? Thanks for all your advice by the way mate, I'm closer to solving this than I was before, because I now have a particular subject to research

#### MarkFL

Staff member
So, if I learn about this stuff, will I (eventually) learn an equation that can I can use to solve this? I'm asking you to give me one, just wondering if it's going to be worth learning about. Is it even possible to solve this in any way other than substitution and elimination? Thanks for all your advice by the way mate, I'm closer to solving this than I was before, because I now have a particular subject to research
There are many ways to solve a linear system, some of which use matrices. It is also possible that your programming language has a system solving function intrinsic to it.

#### dboxall123

##### New member
There are many ways to solve a linear system, some of which use matrices. It is also possible that your programming language has a system solving function intrinsic to it.
OK, thank you very much for your help mate. Now I know what i'm looking at I can start to work something out. Much appreciated

#### soroban

##### Well-known member
Hello, dboxall123!

Two seconds? .Not possible!

. . $$\begin{array}{|c|c|c|c|c||c|} \hline \bigstar & \heartsuit & \Delta & \bullet & & 1434 \\ \hline \Delta & \bigstar && \Delta & \bullet & 1346\\ \hline \heartsuit & \bigstar & \bullet & \bigstar && 1630 \\ \hline \blacksquare & \Delta & \Delta && \bigstar & 1111 \\ \hline \Delta & \bigstar & \Delta & \Delta && 1168 \\ \hline 1142 & 1891 & 1150 & 1346 & 860 & \\ \hline\end{array}$$

$$\text{Let: }\:a = \bigstar,\;b = \heartsuit,\;c = \Delta,\;d = \bullet,\;e = \blacksquare$$

Then we have:

. . $$\begin{array}{|c|c|c|c|c|c|} \hline a&b&c&d&& 1434 \\ \hline c&a&&c&d&1346 \\ \hline b&a&d&a&&1630 \\ \hline e&c&c&&a&1111 \\ \hline c&a&c&c&& 1168 \\ \hline 1442 & 1891 & 1150 & 1346 & 860 & \\ \hline \end{array}$$

From the rows we have:
. . $$\begin{array}{cccc}a+b+c+d &=& 1434 & [1] \\ a+2c+d &=& 1346 & [2] \\ 2a + b+d &=& 1630 & [3] \\ a+2c+e &=& 1111 & [4] \\ a + 3c &=& 1168 & [5] \end{array}$$

From the columns we have:
. . $$\begin{array}{cccc}a+b+2c+e &=& 1442 & [6] \\ 3a+b+c &=& 1891 & [7] \\ 3c + d &=& 1150 & [8] \\ a+2c+d &=& 1346 & [9] \\ a+d &=& 860 & [10] \end{array}$$

Solve the system of equations: .$$\begin{Bmatrix}a &=& 439 \\ b&=& 331 \\ c&=& 243 \\ d&=& 421 \\ e&=& 186 \end{Bmatrix}$$

#### dboxall123

##### New member
Hello, dboxall123!

Two seconds? .Not possible!
Hi soroban. I think you have also misunderstood the challenge. When I (eventually) manage to understand this stuff, I will write a computer program to solve it for me. Of course, I'm not very good at maths, and every site I try to learn from just seems to be adding random numbers and claiming that they are the answer. (I realise this isn't true by the way)