100 Tiles Problem

[Richard Ingalls]

Note: I am posting this here because it seems to my eyes extremely complicated and I do not think it would fit anywhere else, correct me if I am wrong.

This is an interesting problem that I have created that I can not solve, there are just too many combinations and everything for me to be able to figure this out. I am not even sure whether or not it is possible to solve this problem. Here is the problem;

You must fit 150 people in a room. The room is covered in 100 tiles. Each tile must have a certain number of people on top of it, and there must be between 10 and 25 tiles of each color. There are five colors of tiles: red, green, blue, orange, and brown. Red tiles must have zero people per tile, green tiles must have one person per tile, blue tiles must have two people per tile, orange tiles must have three per tile, and brown must have four per tile. What allowed combination of tiles will work?

I hope someone can either solve this or prove that it can't be.

 

[Deleted member 4993]

Note: I am posting this here because it seems to my eyes extremely complicated and I do not think it would fit anywhere else, correct me if I am wrong.

This is an interesting problem that I have created that I can not solve, there are just too many combinations and everything for me to be able to figure this out. I am not even sure whether or not it is possible to solve this problem. Here is the problem;

You must fit 150 people in a room. The room is covered in 100 tiles. Each tile must have a certain number of people on top of it, and there must be between 10 and 25 tiles of each color. There are five colors of tiles: red, green, blue, orange, and brown. Red tiles must have zero people per tile, green tiles must have one person per tile, blue tiles must have two people per tile, orange tiles must have three per tile, and brown must have four per tile. What allowed combination of tiles will work?

I hope someone can either solve this or prove that it can't be.

What is the maximum number of brown tiles that can be used to file the room?

 

[Richard Ingalls]

There must be a total of 100 tiles, and there is a minimum of 10 and a maximum of 25 for any and all tile colors.

 

[blamocur]

Don't have any formal proofs, but my quick and dirty script shows that for 100 tiles the number of people is between 160 and 240.

 

[blamocur]

Don't have any formal proofs, but my quick and dirty script shows that for 100 tiles the number of people is between 160 and 240.

Actually, it makes sens that the minimum number is 0*25 + 1*25 + 2 * 25 + 3 * 15 + 4*10 = 160 and the maxim is 0*10 + 1*15 + 2*25 + 3*25 + 4*25 = 240.

 

[Deleted member 4993]

Note: I am posting this here because it seems to my eyes extremely complicated and I do not think it would fit anywhere else, correct me if I am wrong.

This is an interesting problem that I have created that I can not solve, there are just too many combinations and everything for me to be able to figure this out. I am not even sure whether or not it is possible to solve this problem. Here is the problem;

You must fit 150 people in a room. The room is covered in 100 tiles. Each tile must have a certain number of people on top of it, and there must be between 10 and 25 tiles of each color. There are five colors of tiles: red, green, blue, orange, and brown. Red tiles must have zero people per tile, green tiles must have one person per tile, blue tiles must have two people per tile, orange tiles must have three per tile, and brown must have four per tile. What allowed combination of tiles will work?

I hope someone can either solve this or prove that it can't be.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

 

[Richard Ingalls]

Thank you. Now I know that my problem cannot be solved.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

What I tried is getting a code to print the combination of tiles when it reaches the correct value. The code was flawless, I just didn't know if I had oopsed with my math or not. Now I know that it is impossible to have 150 people in the 100 tile room with the restrictions on tile amounts given.