# Distribution problem

#### herbageonion

##### New member
Hello, this my first post on here so I hope I'm doing this right

I have a problem and I'd really appreciate some help.

I have a number of prizes, 5000, which need to be spread out/distributed over a period of 30 days. I want to award more prizes on day 1 than day 2 and more on day 2 than day 3 etc, also, I want to award more prizes in the first 15-16 days than on the back 15, ultimately, by day 24, there should be the lowest number of prizes remaining. The lowest number can be 0.

Is there any known formula or strategy that would solve this? It sounds like something that probably exists or even has a name.

#### lev888

##### Full Member
Hello, this my first post on here so I hope I'm doing this right

I have a problem and I'd really appreciate some help.

I have a number of prizes, 5000, which need to be spread out/distributed over a period of 30 days. I want to award more prizes on day 1 than day 2 and more on day 2 than day 3 etc, also, I want to award more prizes in the first 15-16 days than on the back 15, ultimately, by day 24, there should be the lowest number of prizes remaining. The lowest number can be 0.

Is there any known formula or strategy that would solve this? It sounds like something that probably exists or even has a name.
Do you want the difference between successive days to be approximately constant? Then look into arithmetic sequences.

#### herbageonion

##### New member
Do you want the difference between successive days to be approximately constant? Then look into arithmetic sequences.
Not necessarily, the difference between successive days would be determined by the input value, I think it would need to decrement on a curve to get to zero after 30 days... is that still an arithmetic sequence?

#### lev888

##### Full Member
What would prevent an arithmetic sequence to decrease to 0?

#### Subhotosh Khan

##### Super Moderator
Staff member
Hello, this my first post on here so I hope I'm doing this right

I have a problem and I'd really appreciate some help.

I have a number of prizes, 5000, which need to be spread out/distributed over a period of 30 days. I want to award more prizes on day 1 than day 2 and more on day 2 than day 3 etc, also, I want to award more prizes in the first 15-16 days than on the back 15, ultimately, by day 24, there should be the lowest number of prizes remaining. The lowest number can be 0.

Is there any known formula or strategy that would solve this? It sounds like something that probably exists or even has a name.
5010/30 = 167

One way would be to go AP and adjust at the end. you could go:

,........

#### Jomo

##### Elite Member
First I would see if this is possible.
I would compute 0 + 1 + 2 +3 +... + 14 +15 + 14 +13 +...+1 = 225. Since 225 <500 it can be done. So what is the problem getting this done?