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Promoting Cuban cigars, are you?
I take it you have not heard of the sieve of Eratosthenes.
I was assuming that the die was rolled simultaneously with the flipping of the coin.
An urn contains 15 balls. There are only 2 different colors the balls can have, red and orange. There are at least 3 of each color in the urn. Picking 3 balls without replacement. the probability that all of the picked ones are red is the same as the probability that exactly one of them is orange. How many of the 15 balls are red?
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Thats quite funny. I think theres a slight typo though. What the narrator said was deaf in two ears (which the other person misheard as dead in two years).
JaneFairfax,
Absolutely amazing! Your scores and times verge on being unbelievable! Hmmm... is there a connection between number theory and being skilled at billards?
When playing any game, you have adopt a specific strategy based on that particular game. For this one, my tips for getting to 2501 or highter would be these:
(1) Go for the highest-scoring pockets.
(2) Go for the most accessible pockets and pot as quickly as possible.
(1) Obviously going for high scores such as 12 × 12 = 144 will advance your total score much more quickly than if you only try low scores like 2 × 2 = 4 (which you would have to do 36 times before your total score advances by 144). However, in some of the table configurations, the highest-scoring pockets may be rather inaccessible. In this case, (2) might be a better option. For instance, suppose the pocket marked 12 on a particular table is in a tricky corner, and it might take you 30 seconds to make a successful pot there. Then you would take one minute to make 12 × 12 = 144. On the other hand, there may be a pocket marked 9 on the same table where you can pot successfully in just 10 seconds. If you go for that pocket four times, you would score 162 in 40 seconds more points in less time than going for the awkward pocket marked 12.
Try and strike a balance between (1) and (2) to get to 2501 as quickly as possible.
For Humphreyss corollary, see this: http://www.mathisfunforum.com/viewtopic … 38#p109938.
For example,
gives the sequence and gives the sequence . You can see that there is a big gap between 9 and 26 where prime numbers can be found.Hint for #1:
Let
be a finite subgroup of where and . Set . Now show that .Hi;
Try this one on for size, it is quite easy. Which is larger and why?
Wow that is cool.
A person reduces the assertion that there is always a square between n and 2n inclusive for all n to this inequality:
Correct proof of #3.
If the statement were false, there would exist a natural number
and a natural number satisfyingWith some simple algebraic manipulation, we should arrive at
It can be easily checked that there are no natural numbers
satisfying for or and so we have a contradiction.Hi;
How would you judge this answer? And why?
I improved my time.
http://www.mathsisfun.com/games/billiard-tables.html
The object is to score 2501 points or more. I completed the game in under 10 minutes.
There is nothing wrong with mods; I use them a lot too. But I also like to keep my mind open for simple solutions, if they exist.