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## #1 2017-03-19 14:39:18

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,858

### A Medley of Melodramatic Problems

1.If $abcd=25!$, then what is the minimum of a+b+c+d?
2.   What is the minimum of $(x+1)^2+(x-1)^2+(x+2)^2+(x-2)^2+(x+4)^2+(x+5)^2$
3. Find the least positive integer n such that n and n+1 have prime factorizations of exactly 5(not necessarily distinct) prime factors.
4.Ted flips five fair coins. The probability of Ted getting more heads than tails is m/n where m and n are relatively prime. Find m+n.
5. What is $2^{2245}+3^{2^{15}}+5^{14}$ mod 14?
6.$\frac{1}{2^2}+\frac{2}{3^2}+\frac{3}{4^2}+\frac{4}{5^2}+\frac{5}{6^2}+\frac{6}{7^2}$
7. Alice chooses 1 positive integer from the set [1,1000]. She chooses another number from that set. What is the probability that the Harmonic Mean + the Arithmetic Mean of these 2 numbers is greater than 510?

The integral of hope is reality.

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## #2 2017-03-19 16:47:59

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 108,496

### Re: A Medley of Melodramatic Problems

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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