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RE: Brainsteem #10 Prize Mathematics Puzzle [Win 2 SBD and 1 SBD]

in #math7 years ago (edited)

The probability of drawing a red ball is originally R/21, and clue "a" reduces that probability by 1/28 after adding balls. The greatest common factor (GCF) of 21 and 28 is 7, which tells me that W must be a multiple of 7. There can't be 21 white balls to begin with, as that would make the probability of drawing a red ball always 0. If W = 14, then R/21 becomes R/35.

R/21 - 1/28 = R/35 -> (20R - 15)/420 = 12R/420 -> 8R = 15 -> R = 1.875.

No good. W = 7.

So trying again with W = 7 resulting in R/21 turning into R/28...

R/21 - 1/28 = R/28 -> (4R - 3)/84 = 3R/84 -> R = 3.

So far, R = 3 and W = 7 (and thus B = 11 as well) looks good. We just need to verify through clue "b". That clue gives us the equality W/21 + 1/18 = W/(21 - R). If we plug in R = 3 and W = 7 and simplify, both sides equal 7/18. Thus the solution has been verified. R = 3, W = 7, B = 11.


On the rewards issue, I think you should stick to the fixed prizes for now, as that seems to be the easiest way for you to handle it. The chainBB Reward Distribution feature should be tested first using a post not involving a puzzle. Maybe something like "comment with an interesting math fact you learned this week". Pick one or two of your favorite responses as winners, and see if the prize(s) distribute as you thought it should. If it works properly on the test post, then you can look into switching back to the percentage method again.

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