Math Is Fun Forum

Hi;

Only if the threatener has information and motives such that he would probably benefit from carrying the threat out.

Hi,

Having thought about it, the case of an odd number of black pills to start with will lead to a 100% chance of the last pill being black.
Think about it - as long as more than one black is in the bottle, a white will be added sooner or later. An odd number of black pills can't all be taken out of the bottle. And inevitably, when one black remains, all the whites will then go.

The probabilities of running out first... that just might require coding ability xP

For anyone who might be interested, the problem is:
Beginning with 218 black and 217 white, what is the probability that 109 black pairs will be drawn before the sum of non-black pairs becomes 217 greater than the number of black pairs?
That will give the probability of black running out first.
It appears to me, intuitively, that the probabilities will be somewhat close to 50-50, but I am not confident of that

Hi anna_gg, I will try to explain what bobbym saw, and I think it will count as a proof that it is white 100%.

First note that a black and white pair and a white pair have the same outcome; one white is removed. Therefore it is only important whether a pair is only black, or not only black.

Since two blacks are removed only when a pair of black pills are drawn, all of the black pills will be gone precisely on the 218/2 = 109th black pair.
All of the whites will be gone when the sum of the black and white pairs and only white pairs is 217 greater than the number of black pairs.

Working out the probabilities of one colour running out first is an interesting problem in its own right, but the question is what colour is the single remaining pill.
Assume that all the whites do run out. Then one white will be added and two blacks subtracted because the next pair will be only blacks. Since it is always two blacks that are subtracted, for this problem the number of black pills must always be even; therefore if there is one pill remaining, it cannot be black.

Furthermore, it is certain that if the game is played long enough, there will eventually remain one white pill. This is because, no matter how many times white runs out, they will just keep replenishing from the extra stock until all the black pills are gone.

Hi;

I assume you want the discriminant to equal zero:

I do not think it is a serious handicap to communication, just as long as people are aware of it (:

I am technically still locked out, but I have unrestricted access simply by changing my network.

Hi bobbym,

It is theoretically possible that none of the first 217 pairs are two blacks, in which case all of the whites will be gone. I think this disproves your hypothesis, although the odds are evidently stacked heavily against a final black pill.

The problem seems to be all about the frequency of all-black pairs to non-all-black pairs. There must be very few of the former for the final pill to be black.

That is extremely cool.

But how did you "generate" the first line?

The word pokr. I see.
I think I might be locked out, but I can access the forum on my phone (on which I use a relatively unknown browser)

It's a funny bug, lol. It seems that casinno is not a favoured word either

Hello

2 + 9/9 + 9 + 1

Hi;

Is 0x^2 + 0x + 0 a quadratic equation? Hahaha

Hello;

I have made an attempt! The result might be slightly too ugly to be correct, but even if it is not, I enjoyed the problem.

The only disclaimer is that we are not told explicitly which side lengths of the body are the width, height and length; but from plain common sense, and also from the face that would include the head, hopefully we may deduce it and my logic is correct.