# Maths Problem Watch

Imagine the values of numbers (1-5) on the top row is not known. Only thing you know is that some have a high value (3, 4, 5) and are rare. The second group has a low value (1, 2) but they are more frequent. On the remaining rows, each one of them may/may not be present and you only know the sum of each row.

I was just wondering if there is a way to predict the high value numbers just from this information.

It would be great if someone can give me some insights on this problem. I am not a mathematician and I'm sorry if this makes no sense...
Attached Files
2. Maths Problem.xlsx (8.8 KB, 80 views)
3. (Original post by borntodream)

Imagine the values of numbers (1-5) on the top row is not known. Only thing you know is that some have a high value (3, 4, 5) and are rare. The second group has a low value (1, 2) but they are more frequent. On the remaining rows, each one of them may/may not be present and you only know the sum of each row.

I was just wondering if there is a way to predict the high value numbers just from this information.

It would be great if someone can give me some insights on this problem. I am not a mathematician and I'm sorry if this makes no sense...
Ok, from what I understand the top row contains several numbers between 1 and 5. Then for each row below, you highlight some of the cells in red. For each red cell in that row you take the corresponding number from the top row, then add together each number taken to make the row sum.

So are you asking about the case in which the row sums and the position of the red cells is known, but the numbers in the top row are not known?

One approach you could take is to solve simultaneous linear equations to get the numbers in the top row.

If you're doing this by hand then it looks like it might be best to start off with the rows with small row sums, so that you can determine the numbers in the top row that are associated with that row. Knowing that the numbers have to be integers from 1 to 5 would help you to do this.

Knowing that some numbers are 'rarer' than others won't help much although if you have concrete information about perhaps their frequency then that would be useful.
4. (Original post by ttoby)
Ok, from what I understand the top row contains several numbers between 1 and 5. Then for each row below, you highlight some of the cells in red. For each red cell in that row you take the corresponding number from the top row, then add together each number taken to make the row sum.

So are you asking about the case in which the row sums and the position of the red cells is known, but the numbers in the top row are not known?

One approach you could take is to solve simultaneous linear equations to get the numbers in the top row.

If you're doing this by hand then it looks like it might be best to start off with the rows with small row sums, so that you can determine the numbers in the top row that are associated with that row. Knowing that the numbers have to be integers from 1 to 5 would help you to do this.

Knowing that some numbers are 'rarer' than others won't help much although if you have concrete information about perhaps their frequency then that would be useful.
Hello. Sorry for my insufficient explanation but yeah, you understood it correctly. I did think of it doing that way but I don't think it'll work.

Also, on a side note, this is just a simplified version of what I'm planning to do and numbers are not actually integers. Some have a higher value and some a lower value. I am just trying to predict which ones would have the high value...
5. (Original post by borntodream)
Hello. Sorry for my insufficient explanation but yeah, you understood it correctly. I did think of it doing that way but I don't think it'll work.

Also, on a side note, this is just a simplified version of what I'm planning to do and numbers are not actually integers. Some have a higher value and some a lower value. I am just trying to predict which ones would have the high value...
How many numbers and rows are involved, and how are the positions of the red cells chosen? Are they chosen at random or in a specific way? Also when you say this is a simplified version, do you mean the actual problem you're solving has more/larger numbers involved or are there other complications?

In general, solving linear simultaneous equations would work for this, provided you have sufficiently many rows and that the red cells are not arranged awkwardly. If there are a lot of rows/numbers involved then this could be solved by a computer.

However, if solving simultaneous equations does not solve your problem fully then you may need to look into using what you know about the unknown numbers in the top row. If some are high and some are low then does this mean that there is an 'in between range' in which the numbers cannot lie? Are the numbers chosen at random, or through some other method? If they're chosen at random, are they independent, and how are they distributed? Whilst knowing this information may not completely solve your problem, you might at least get an idea of which solutions are more likely, which may help you.
6. I don't know how many different numbers are involved and I have no idea of their value. The number of rows would possibly be ~10 and columns ~50. Red cells are distributed randomly. The actual problem would not involve integers.

The reason why I said high/low values is because I don't need to know their absolute value and I'm not sure about the range. I just want to estimate which ones have most effect on the outcome (sum) i.e. find the high values.
7. (Original post by borntodream)
I don't know how many different numbers are involved and I have no idea of their value. The number of rows would possibly be ~10 and columns ~50. Red cells are distributed randomly. The actual problem would not involve integers.

The reason why I said high/low values is because I don't need to know their absolute value and I'm not sure about the range. I just want to estimate which ones have most effect on the outcome (sum) i.e. find the high values.
Since you don't have enough rows, then that would rule out simultaneous equations.

You may well find that you can't work out exactly which numbers are high, but you could narrow it down to several possibilities. What you could try is for each red cell calculate the row sum divided by the number if red cells in that row. This will give an estimate of the value in the top row above that red cell. Then for each column, take a weighted average of the estimates for the unknown number in the top row. Weight cells corresponding to rows with fewer red cells more heavily since they would be more specific about the columns they refer to.

Then, look at the average estimates to get an idea of which of the unknown numbers are likely to be large. The estimates would tend to shift the larger and smaller numbers closer together but you're not worried about that.

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