not homework, i'm a lawyer, not a mathematician

trying to figure out something that works here.

3 levels

2400 * x
2250 * y
2100 * z

sum of all = 250,000,000

x < y < z

I'm relatively close with something like 18,000 , 36,000 , 60,000

Ideally the spreads between numbers would be somewhat close like that, and the more zeroes at the end of each number the better. Don't want something like 19,157 / 33,562 etc.

Is there any easy way to do this? I am just trial and error'ing now and it's frustrating.

Thanks. I'll send some ethereum to whoever can help out.

if you respond, please pm me or quote part of my message so i get an alert on my phone. much appreciated!

I've been advised elsewhere this isn't possible.

2400, 2250, 2100 were based as 60-40% bonuses on 1500.

Im happy to move those amounts to 55, 50, 45% or 50,45,40 or 55,45,35 if that makes the math work.

Thanks.

Can you offer some context in case we are not working on something sensible (like why the numbers have to be that way with many zeroes) ?

For example requiring to have exactly 250000000 that way from this linear combination can be doable eventually with some numbers that have several zeros which i imagine you want to be there to have some plausibility of rounding numbers argument as reported from the source. But in that case you introduce an implausibility for the sum of 3 so unique up to 3-4 non zero digit numbers to lead to exactly 250000000 (a very special number given all else) . Are you seeing now this is as rather plausible outcome that 3 numbers conspire so nicely to give exactly 250000000 or is the process such that 250000000 is a natural cutoff that terminates things once reached anyway. Only if all 4numbers are rounded this makes sense but still leaves some room for criticism on why 250 mil is so fine tuned vs the others or the reverse why the others are so fine tuned to give that number with so many zeros compared to them.

Context.

There are 1 billion units.

25%: 250 million are being sold at a bonus price.

The base price is 1500 units per dollar.

So at 60,50,40% bonus that equates to 2400, 2250, 2100 per dollar.

Im trying to find how many at each bonus rate to distribute.

The higher bonus needs to distribute less than the next, and so on.

Ideally bonus =< 60% and =>30%

I don't want too big a spread between the bonuses. Like 5-10% diff max per level.

I had it work at 60% 50% 33.33% but it was too big a drop off.

Thanks.

So are you trying to see how to arrange the bonuses 60 to 30 a<b<c so that a,b,c are close to some round numbers with many zeroes.

Therefore your 2400, 2250 and 2100 are not set in stone they can also move a little bit provided they remain in 60-30 range.

The objective is to have all these the number of bonuses and the bonus % themselves not be very many digits numbers but multiples of 10 or 100 or so if possible. Like 60% is ok 55% is ok but 59% is not ok?

Yup exactly masque

Your original setting has no solution because 2400 2250 and 2100 have all a factor of 3 in common but 2500000000 doesnt.

So one must start by factoring 250000000=25*10^7=5^2*2^7*5^7=2^7*5^9
So your problem is that the unit 1500 has a factor of 3 and it will never work.

Can you change the unit price from 1500 to 1250 or anything that wont have all 3 prizes have common factors the 250mil wont have?

Alternative would be to have bonuses that are multiples of 1/3 like 8/12= 66.67%, 5/12 41.67%, 4/12 33.33%.

Thanks mask.
We can change it to 2350, 2250, 2150 or something similar. Well ideally %s of 1500 that end in 0 or 5.

We could move that 1500 to 1400 I guess. Don't want to go lower.

No not 1400. 1400 introduces 7 as common factor to all 3prizes and now it cant happen again to add up to 250 mil.

You need to have a unit price of only factors of 2 and 5 or to kill some of the other factors by the choice of percentages awarded but that will mean dividing by some stupid numbers that wont ever give you round percentages.

Try unit price 2^x*5^y with x, y less than 7 and 9.

Like say 1600. This is 2^6*5^2. Or go to 1250


Now you can have for example 1.6* 1600=2560, 1.45*1600=2320 and 1.3*1600=2080.

Easily many solutions now like say 15000 41000 56000 per prize among many others (eg 17000, 37000,58000 or 18000,35000,59000).

thanks masque. pm me your eth address if you have one.

Thanks but its ok its no big deal. Do you have a way to manipulate the 250 mil to something a little different that has more factors? Then it might be possible to get closer to your initial base value.