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Grid of numbers and dashes, X-Akseli and Y-Ehe?

Puzzling Asked by user36160 on March 15, 2021

I have been given this puzzle by my friend (who is a qualified military cryptographer). I am completely stuck as for what to do.

They gave me this hint:

"Don’t take it so literal, think in all three dimensions."

What if it isn’t a grid we are looking at – what if it’s a cube?

Another hint:

"The puzzle was made on physical paper, I also solved it on physical paper Even when I made the solution to show Llama, I had to print out my digital spreadsheet for physical paper(edited) because only physical paper has three dimensions"

I have no idea where I’m going with this

enter image description here

2 Answers

I've tried a few things, but haven't got that much, maybe someone can develop on this or find something I missed.

First off, using the numbers as $x$ and $y$ coordinates we can plot a scatter graph:

enter image description here

But as you can see there is very little correlation. Indeed using a spearman's rank calculator, we get a value of $-0.109244$:

enter image description here

So very little negative correlation.

All I can think off for the table, is that perhaps the values in each cell is $sqrt{a+b}$ with $a$ being the corresponding horizontal value and $b$ the corresponding vertical value.

However this really doesn't give a nice table.

The last thing I tried was superimposing the graph on to the table:

enter image description here

Doesn't really give anything...

What I find really suspicious is that there are 9 x values and 9 y values.

However, despite these attempts I was unable to find anything. The only thing I can think of which I am sure about is the values for the diagonal cells ($-x$ means that the cell is a path and has an integer $x$.

Here is a copyable mathjax table:

$$begin{array}{|c|c|c|c|c|c|c|c|c|c|} hline & text{1} & text{2} & text{3} & text{4} & text{5} & text{6} & text{7} & text{8} & text{9} hline text{1} & 1 & - & & - & - & - & - hline text{2} & & -2& & - & & & - & - & - hline text{3} & & - &-3 & - & & & & & - hline text{4} & & & & 4 & - & - & & & - hline text{5} & & & - & - & 5 & - & & - & - hline text{6} & - & - & - & & & 6 & & - & hline text{7} & - & & - & - & - & - & -7& - & hline text{8} & - & & & - & & & & -8& - hline text{9} & - & - & - & - & & & & & 9 hline end{array}$$

Answered by Beastly Gerbil on March 15, 2021

The first thing to notice is that the the values of Y-ehe are multiples of the corresponding row. 45 is a multiple of 9, 40 a multiple of 8 and 14 a multiple of 7, etc.

The other thing is that the X-akseli and Y-ehe values sum up to the same value, 194.

If you look at the matrix, you see that the multiples in Y-ehe almost match the number of blank cells. There are 2 empty cells in row 7 and Y-ehe(7) is 2x7. So if you fill the blank cells with the row number, the cells in a row nicely sum up to the Y-ehe value.

Naturally you will want to compute the column sums, and you discover the X-akseli values.

enter image description here

Note however that you have to remove the initial 6 to make it work. Probably a typo.

All this teaches us one thing: the value of a cell is the row number.

Now I will boldly assume, out of nowhere, that the goal is to go from the top-left to the bottom-right corner by minimizing the total cell count. Here are 2 options:

enter image description here and enter image description here

The number at the bottom-right is the sum of all cells. As you can see, the second path, with a score of 80, is better than the first one, with a score of 82. It is longer but uses smaller cell values. There are other paths, but they result still larger scores. The solution on the right shows the optimal path.

I have no explanation about the mismatched sums or where the hint "Think in all 3 dimensions" comes into play.

Answered by Florian F on March 15, 2021

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