| 4 |
riddles / putnam exam (pure math) / Re: Zero? |
Today at 8:52am |
| Started by kyle1080 | Last post by Michael Dagg |
> OR x=0
True, but the trivial solution is not representive of
all solutions.
> There is no function in the problem having the
> independent variable x, unless you use x3 as
> function, like f(x)=x3.
Not necessary. You may want to review differentiation
and integration. |
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| 5 |
riddles / easy / Re: Stray |
Today at 5:42am |
| Started by Iceman | Last post by Grimbal |
You can test them. Walk a few steps and touch a leave. If you move back to the center, you have a magic one. And you might suffer hearing loss from the nearby implosion of the bubble of vacuum that appeared where you disappeared.
This being said, I am not sure that "there are leaves everywhere" and "Both paths have magic that prevents leaves to fall on them." can both be true.
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| 6 |
riddles / easy / Re: Age Polynomial |
Today at 3:48am |
| Started by ThudanBlunder | Last post by ThudanBlunder |
Another way is to observe that if two numbers such as a and b are successively substituted for x in any polynomial with integer coefficients, the difference between the two results will be divisible by a - b. This is because the constant disappears and each of the other terms will be a constant times the difference between equal powers of a and b.
So letting Johnny's age be J and the larger guess be L, we have
L - 7 divides 8
J - 7 divides 77
J - L divides 85
7 < L < J
It follows that L must be 8, 9, 11, or 15
and J must be 14, 18, or 84
And J - L divides 85 implies L = 9 and J = 14
After -3x2 + 52x - 140 I think the next polynomial is x3 - 33x2 + 339x - 1022
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| 7 |
riddles / cs / Re: Median of Stream of data |
Today at 2:49am |
| Started by Erik | Last post by Hippo |
There is a lot of O(log n) solutions (for example balanced "search" trees).
The question is ... is the  (log n) required?
Yes, it is:
0 n;x1,x2,...,xn; 2n is a sequence of 4n inserts and 2n medians giving nx0 and sorted xi's. So based on comparisons the  (n) inserts and medians require (n log n) ... as we know we cannot sort faster based on comparisons. |
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| 8 |
riddles / general problem-solving / chatting / whatever / Re: Rubik's Cube as a 2D puzzle (is this new?) |
Nov 22nd, 2009, 6:53pm |
| Started by amichail | Last post by dmeade |
[quote author=Hippo link=board=riddles_general;num=1233694593;start=0#8 date=04/05/09 at 08:42:24]
Yes, well nor so new, i was watching a video on it last week and it looks great, thougfhg it doesnt seem very easy to me.
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