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Math Puzzles *UPDATED*

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Originally posted by: Vertimus
Originally posted by: chuckywang
Originally posted by: Vertimus
Originally posted by: chuckywang
Originally posted by: Vertimus
Originally posted by: chuckywang
Originally posted by: Vertimus
Originally posted by: chuckywang
1) This is so easy, I'm not going to even attempt it.
2) k=399, I think.
3) 100
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2 and 3 are wrong.
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Whoops. No. 2) k=112.
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DINGDINGDING!!! correct! :thumbsup:
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Prob. 3) 156
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Yep!

LOL... no wonder you got so many of these... you go to imsa!

On the other hand, I think you should probably stop answering for a while... maybe give others a chance 😛
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How did you know about imsa? I didn't think many people knew about it outside of IL.
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Teh Noah sheets 😛
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Nice! I never thought that I'd here about those outside of IMSA or Illinois schools. I never knew those sheets were that famous. I think once I discovered a mistake about them, but I don't remember too clearly.
 
Originally posted by: Vertimus
Originally posted by: JujuFish
7901234568
8*987654321
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The first two numbers aren't divisible by 2. (79 is odd.)
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I was referring to:

Easy: Let N be the greatest integer multiple of 8, no two of whose digits are the same. Find N.
 
Originally posted by: Vertimus
Hard: Given that log(sin x)+log(cos x)=-1 and that log(sin x+cos x)=1/2*(log n -1), find n. (We are assuming base 10.)
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Is that [log (n) - 1] or [log(n-1)]?

If it is the first, n=12. If it is the latter, n=2.2.

 
Originally posted by: JujuFish
Originally posted by: Vertimus
Originally posted by: JujuFish
7901234568
8*987654321
Click to expand...

The first two numbers aren't divisible by 2. (79 is odd.)
Click to expand...

I was referring to:

Easy: Let N be the greatest integer multiple of 8, no two of whose digits are the same. Find N.
Click to expand...

Oh, i didn't see that. However, that's still incorrect.
 
Originally posted by: dullard
Originally posted by: Vertimus
Hard: Given that log(sin x)+log(cos x)=-1 and that log(sin x+cos x)=1/2*(log n -1), find n. (We are assuming base 10.)
Click to expand...
Is that [log (n) - 1] or [log(n-1)]?

If it is the first, n=12. If it is the latter, n=2.2.
Click to expand...

It's log (n)-1.

12 is right.

Good job!
 
please post the explanations too. I would like to know a neat way of solving these puzzles without using "brute force" algorithms.
 
Originally posted by: whitecloak
please post the explanations too. I would like to know a neat way of solving these puzzles without using "brute force" algorithms.
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Is there a specific one you would like the solutions to? I don't think I have time to write solutions for more than a few.
 
From now on, any solution must have a short description along with it. I dont' need a proof, but a short explanation would work. Of course, hard problems should have longer explanations than easy problems.
 
Ooooh. I read 8 wrong. I thought it meant: if the number was 81649 then 8 was a perfect square, 81 was a perfect square, and 816, 8164, etc..
 
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