Search found 1804 matches

by Nitrodon
Wed Apr 12, 2017 12:57 am UTC
Forum: Logic Puzzles
Topic: Two secrets
Replies: 20
Views: 4904

Re: Two secrets

I think I have an O(log(N)) solution. Let A initially be {1, 2, 3, ..., N-1}. At all times, we know that at least one of the numbers is in A. Divide A into three roughly equal sets A 1 , A 2 , and A 3 , and ask about A 1 ∪ A 2 , A 1 ∪ A 3 , and A 2 ∪ A 3 . If we get a "yes" response to one...
by Nitrodon
Sun Mar 26, 2017 5:36 pm UTC
Forum: Mathematics
Topic: An annoying derivative
Replies: 4
Views: 2470

Re: An annoying derivative

Oops. I saw that the inner function (2/π) · ( arcsin(x) + x · √(1 - x²) ) was differentiable at 1, then got stupid and assumed that meant t was also differentiable. I have still proven that y'(1) = 1 is equivalent to "the derivative of (1-t) 3/2 at x=1 is zero". It is possible to prove the...
by Nitrodon
Mon Feb 27, 2017 2:44 am UTC
Forum: Mathematics
Topic: An annoying derivative
Replies: 4
Views: 2470

Re: An annoying derivative

The proof of the product rule can also be used to show that if y(x) = u(x) · v(x) where u(c) = 0, u is differentiable at c, and v is continuous (not necessarily differentiable) at c, then y is differentiable at c, and y'(c) = u'(c) · v(c). This can be used to get rid of the annoying 0/0 terms obtain...
by Nitrodon
Sun Oct 16, 2016 11:44 pm UTC
Forum: Mathematics
Topic: "Identical" sequences generated by 2 different methods
Replies: 2
Views: 1068

Re: "Identical" sequences generated by 2 different methods

If p is prime, then phi(p) is simply p-1. Let k = int(sqrt(p)). When k divides p-1, we have p = kd + 1 for some integer d.

Given k, what bounds can you place on d?

Where are the right angle turns in the Ulam spiral?
by Nitrodon
Thu Jul 28, 2016 6:48 pm UTC
Forum: Mathematics
Topic: Goahead52's Math Posts
Replies: 148
Views: 12424

Re: Theorem and consequences

Indeed, the theorem can be proven. The case x=1 is trivial. Assume x>1, and let z be the positive real number satisfying z^(k+1) = x^k. Then z = x^[k/(k+1)] < x, and thus (x+1)/x < (z+1)/z. Hence [(x+1)/x]^k < [(z+1)/z]^k < [(z+1)/z]^(k+1). Multiplying by x^k = z^(k+1), we obtain (x+1)^k < (z+1)^(k+...
by Nitrodon
Fri Jul 08, 2016 1:22 am UTC
Forum: Forum Games
Topic: Count up with the Five Fives puzzle
Replies: 298
Views: 15789

Re: Count up with the Five Fives puzzle

61 = 55 + 5 + 5/5
by Nitrodon
Sun Jul 03, 2016 9:21 pm UTC
Forum: Forum Games
Topic: Count up with the Five Fives puzzle
Replies: 298
Views: 15789

Re: Count up with the Five Fives puzzle

44 = 55 / (5 * .5 * .5)
by Nitrodon
Sun Jul 03, 2016 1:33 am UTC
Forum: Forum Games
Topic: Count up with the Five Fives puzzle
Replies: 298
Views: 15789

Re: Count up with the Five Fives puzzle

Might as well put this new function to use.

42 = 5! * (.5/5 + .5*.5)
by Nitrodon
Fri Jul 01, 2016 10:27 pm UTC
Forum: Forum Games
Topic: Count up with the Five Fives puzzle
Replies: 298
Views: 15789

Re: Count up with the Five Fives puzzle

39 = (5 * 5 - 5.5) / .5
by Nitrodon
Wed Jun 29, 2016 5:06 am UTC
Forum: Forum Games
Topic: Count up with the Five Fives puzzle
Replies: 298
Views: 15789

Re: Count up with the Five Fives puzzle

35 = 55 + 5 - 5*5
by Nitrodon
Sun Jun 26, 2016 3:48 am UTC
Forum: Forum Games
Topic: Count up with the Five Fives puzzle
Replies: 298
Views: 15789

Re: Count up with the Five Fives puzzle

33 = 55 * (.5 + .5/5)
by Nitrodon
Sat Jun 04, 2016 5:35 am UTC
Forum: Mathematics
Topic: distance between two vertices in a random binary tree
Replies: 1
Views: 1691

Re: distance between two vertices in a random binary tree

The factors (1 - 1/(n-j choose 2)) in that last line can be manipulated into a form that makes them much easier to multiply together.
by Nitrodon
Tue Mar 22, 2016 2:38 pm UTC
Forum: Mathematics
Topic: Colliding Missles
Replies: 11
Views: 3009

Re: Colliding Missles

You seem to have made some arithmetic errors in dividing by 60. The correct speeds are 350 and 150 miles per minute, which do indeed add up to 500.

The comma in 9000 (along with the initial distance, which is either 1323 or 5323) allowed the filters to change the first digit.
by Nitrodon
Sun Feb 28, 2016 6:10 am UTC
Forum: Forum Games
Topic: Count Up in Balanced Base 5
Replies: 43
Views: 2446

Re: Count Up in Balanced Base 5

222
by Nitrodon
Sat Feb 27, 2016 5:19 am UTC
Forum: Forum Games
Topic: Count Up in Balanced Base 5
Replies: 43
Views: 2446

Re: Count Up in Balanced Base 5

220
by Nitrodon
Fri Feb 26, 2016 9:17 pm UTC
Forum: Forum Games
Topic: Count Up in Balanced Base 5
Replies: 43
Views: 2446

Re: Count Up in Balanced Base 5

222
by Nitrodon
Thu Feb 25, 2016 8:45 pm UTC
Forum: Forum Games
Topic: Count Up in Balanced Base 5
Replies: 43
Views: 2446

Re: Count Up in Balanced Base 5

112
by Nitrodon
Tue Feb 09, 2016 9:27 pm UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 73576

Re: Count Up with the Four Fours Puzzle

490 = (((√!4)!)!! + !√4) * (4!! + √4)
by Nitrodon
Sun Feb 07, 2016 7:51 am UTC
Forum: Forum Games
Topic: My Number Is Not Your Number!
Replies: 168
Views: 15164

Re: My Number Is Not Your Number!

-12345.6789

The previous number was an integer, and this is not. Thus, they are different.
by Nitrodon
Sat Feb 06, 2016 11:11 pm UTC
Forum: Mathematics
Topic: Coin flip problem
Replies: 6
Views: 1415

Re: Coin flip problem

This is a trick I learned once for the "drunkard's walk" formulation. Let X k equal the number of heads minus the number of tails after k tosses. The probability that X k stays below m forever is equal to P(X n < m) - P(X n < m and X k = m for some k). For each sequence of flips in the lat...
by Nitrodon
Fri Feb 05, 2016 9:57 pm UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 73576

Re: Count Up with the Four Fours Puzzle

486 = √4 * !4!√4/.4
by Nitrodon
Mon Jan 18, 2016 9:13 am UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 73576

Re: Count Up with the Four Fours Puzzle

301 = !(4 + √4) + (4 * !4)
by Nitrodon
Mon Jan 18, 2016 8:21 am UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 73576

Re: Count Up with the Four Fours Puzzle

299 = (4! - !√4) * (!4 + 4)
by Nitrodon
Sun Jan 17, 2016 11:43 pm UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 73576

Re: Count Up with the Four Fours Puzzle

297 = !4 * 4! + √!44
by Nitrodon
Sun Jan 17, 2016 7:28 pm UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 73576

Re: Count Up with the Four Fours Puzzle

293 = (!4 + 4!!)√4 + 4
by Nitrodon
Sat Jan 16, 2016 7:20 pm UTC
Forum: Logic Puzzles
Topic: Defective Circuit Board Puzzle
Replies: 7
Views: 2378

Re: Defective Circuit Board Puzzle

A lower bound: Without loss of generality, the first test is (1,2,3), and 1 was identified as defective. If board 1 is indeed defective, the other defective board can be anything (9 possibilities). If board 1 is not defective, then the two defective boards can be anything from (4...
by Nitrodon
Fri Jan 15, 2016 12:08 am UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 73576

Re: Count Up with the Four Fours Puzzle

289 = (4!! + !4) * (4!! + !4)
by Nitrodon
Thu Jan 14, 2016 9:40 pm UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 73576

Re: Count Up with the Four Fours Puzzle

287 = √!4 * (!4 - √4)! - !(4!!) = 15120 - 14833
by Nitrodon
Thu Jan 14, 2016 12:43 am UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 73576

Re: Count Up with the Four Fours Puzzle

281 = (!4)!/4! - !(4!!) - (√!4)!
by Nitrodon
Wed Jan 13, 2016 7:42 pm UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 73576

Re: Count Up with the Four Fours Puzzle

277 = 44 + 4! - √!4
by Nitrodon
Wed Jan 13, 2016 2:41 am UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 73576

Re: Count Up with the Four Fours Puzzle

270 = !4 * √(4! + !√4) * (√!4)!
by Nitrodon
Tue Jan 12, 2016 8:31 pm UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 73576

Re: Count Up with the Four Fours Puzzle

266 = !(4+√4) + 4/4
by Nitrodon
Sun Jan 10, 2016 7:05 am UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 73576

Re: Count Up with the Four Fours Puzzle

249 = 4! * (4!! + √4) + !4
by Nitrodon
Sat Jan 09, 2016 8:00 am UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 73576

Re: Count Up with the Four Fours Puzzle

247 = (!4)(!√4)/.4 + 4
by Nitrodon
Fri Jan 08, 2016 8:48 am UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 73576

Re: Count Up with the Four Fours Puzzle

241 = (4!!)!! + !√4 - 4! * (√!4)!
by Nitrodon
Fri Jan 08, 2016 4:37 am UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 73576

Re: Count Up with the Four Fours Puzzle

239 = 4! * (4!! + √4) - !√4
by Nitrodon
Thu Jan 07, 2016 7:03 am UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 73576

Re: Count Up with the Four Fours Puzzle

237 = √!4 * ((!4)√4 - √4)
by Nitrodon
Wed Jan 06, 2016 10:33 pm UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 73576

Re: Count Up with the Four Fours Puzzle

235 = √!44!!-√!4 - 4!!
by Nitrodon
Wed Jan 06, 2016 8:14 am UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 73576

Re: Count Up with the Four Fours Puzzle

226 = 4!! * (4! + 4) + √4
by Nitrodon
Wed Jan 06, 2016 4:40 am UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 73576

Re: Count Up with the Four Fours Puzzle

224 = 4 * (4√!4 - 4!!)

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