you are given a list of 100 coordinates, and asked to use the pathageoran theorm he fewest number of times to determine the shortest distance between any two. is it an n^2 problem, or can you do better? how much better?
an item is originally priced at 75$. the store advertises a buy one get one free, that you wouldn't mind taking advantage of, plus you have a coupon for 10% off. how much do do you actually purchase the two items for?
inspired by BMADS topic,
1) what's the smallest product of 3 primes that's larger than the sum of each prime number squared?
2) whats the smallest prime number cubed where the digits add up to the original prime?
3) how many prime numbers are equal to the sum of at most 25 primes less than 100?
i've never played a mafia before, but i'll give it a go.
1. Flamebirde
2. BMAD
3. phil1882
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Backups
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Hopefully this will reboot the mafia section. Thanks for the reserve Magic!
EDIT:extra space.
ah i see where i made my mistake.
i assumed height is always (1/2 base)^2 - other side^2
which isn't necessarily so.
(only true for isosceles triangles or equilateral.)
currently i'm studying the sequence
1 2 3 5 7 8 11 12 13 17 19 20 23 27 28 29 30 31....
which is the odd product of prime numbers.
i'm curious to know if there is a good counting function for the number of them below say 10,000,000.
if so, can it be reversed to find approximately the nth odd product?
nicely done for 2.for seven i'm not sure if thats what hes asking.
i think he means that if n is abundant, then it must not have one prime raised to some power.
that is if n is abundant, it must be something like 2^4*3^2*5^3....
but i agree based on 2 its definitely false.
take a number, greater than 1.
if odd, subtract 1, square it.
if even, divide by 2.
2 -> 1
3 -> 4 -> 2
5 -> 8 -> 4
7 -> 36 --> 9 -> 16 -> 8
11 -> 100 -> 25 -> 576 -----> 9
13 -> 144 ----> 9
will this always hit a power of 2?
since random is the optimal strategy, the best way to beat it is to be random yourself.
the chances of winning 15 in a row are roughly (1/3)^15 = .0000006969 %
which means you should do so after roughly 1 million games.