integer
Suppose X is a positive integer, and R a positive real number.
If ROUND(XR) = M, and integer then XR - M <= 0.5 or X - M/R <= 0.5/R ...(1)
ROUND(ROUND(X*R)/R) = N say, an integer. then M...
...n-1) * (n-2) * (n-3) * (n-4) * j
It's not hard to generalize it so it will produce any 'next integer in the sequence' that you desire. That means that if you give me *any* finite se...
This thread reminds me of the old proof that there exists no smallest uninteresting integer. Thus, each integer is interesting.
Proceed in order from one upward through the integers, assessing whe...
...le options are as follow:
Strategy (A): The first winning ball will have the serial number that is the integer part of the half of the first drawn ball's serial number. The second winning bal...
Second differences between successive integers cubed equal successive multiples of 6:
. . . -27 19 -8 -12 7 -1 -6 1 0 0 1 1 6 7 8 12 19 27 18 37 64 . . .
This should be enough insight to prove...
...H_3 is an altitude of triangle AH_1H_2.
Etc.
a) Find the length of AH_(2n-1) where n is a positive integer.
b) Find the length of AH_(2n) where n is a positive integer
Have fun! Bob St...
...ow is my purported result; 'value1' is a check (should be 1/2.)
program buffon implicit none integer, parameter :: dp = selected_real_kind(15,300) real(dp) :: num...
It's in the Encyclopedia of Integer Sequences: http://www.research.att.com/cgi-bin/access.cgi/as/njas/
sequences/inde... ID # A006933.
Each integer from 1 to 36 is associated with a letter (a, b, or c) as given below.
Place the integer/letter combinations ('ILC's) into the spaces (one ILC per space) of a 6-by-6 grid suc...
...villages, townships, islands, etc.
About what percent of the entries would you estimate begin with the integer ‘1’? By what thought process did you arrive at your estimate?
Bill Ryan...
Let Fib(1) = Fib(2) = 1 , and for i any integer > 2, Fib(i) = Fib(i - 2) + Fib(i - 1).
That is, Fib(n) is the Fibonacci sequence.
Now, let S(n) = Fib(1) / 2^1 + Fib(2) / 2^2 + ... + Fib(n) ...
...it only gives a solution for certain 'nice' n's; particularly:
n = (3^w - 3)/2 for some integer w
What if you had to find the counterfeit amongst 100 coins? NOT 120, which would...
Okay, this idea is a work in progress.
Let n be some positive integer. (The best n is unknown to me.) Each player gets one of two identical pieces of n-by-n graph/tracing-paper. (The top of each p...
...re special cases to terminate the recursion, but I think our operator is quite fully defined, for k as any integer, positive or negative, and m, n as any positive integers.
Formally, it's...
...ation, the divide and conquer paradigm, program development methodology, constraint satisfaction problems, integer programming, and specification....
... finite number of words which have a currently acknowledged meaning.
Thus, for eanch strictly positive integer n, there are a finite number of questions consisting of n words.
The union of fin...
...are A with E, and B with D.
Extension: Let's say we have n numbers to sort. Let c be the smallest integer such that 2^c >= n!. Can we always find a way to sort n numbers with c comparisons...
...g=Grampa's age * t=Ted's age * * data: * Ted is older than Pete * t * p = g * t + p + g = 90
integer p,t,g
for p=1 to 90 for t=1 to 90 for g=1 to 90 if t*p=g then if t+p+g=90 then if...
...ing it, then performing this operation *twice* should yield a fourth power. In this case there would be no integer solutions to the problem though....
...ld being 25 or greater.
Thus each boy grabs n, each girl n+25, and they end up with n+12 each; n is an integer between 1 and 12 inclusive.
Revised puzzle:
In this case we have the addition...
Yes, the probabilities given assume that each player chooses from the available squares at random (with equal probabilities). The enumeration of possible games is just that: a tallying of all possible...
***** [SPOILER on “follow-up” problem is at end of this posting.]
The well-known solution is to pass on the first 100/e (37) daughters and then select the next dowry (if any) that is the highe...
This is a repost of the Rare Entries contest originally posted February 24th, AD 2001.
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23rd, AD 2001, GMT -8 (Pacific St...
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