Search found 1804 matches

Wed Apr 12, 2017 12:57 am UTC
Forum: Logic Puzzles
Topic: Two secrets
Replies: 20
Views: 6228

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...
Sun Mar 26, 2017 5:36 pm UTC
Forum: Mathematics
Topic: An annoying derivative
Replies: 4
Views: 2760

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...
Mon Feb 27, 2017 2:44 am UTC
Forum: Mathematics
Topic: An annoying derivative
Replies: 4
Views: 2760

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...
Sun Oct 16, 2016 11:44 pm UTC
Forum: Mathematics
Topic: "Identical" sequences generated by 2 different methods
Replies: 2
Views: 1171

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?
Thu Jul 28, 2016 6:48 pm UTC
Forum: Mathematics
Replies: 148
Views: 14029

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+...
Fri Jul 08, 2016 1:22 am UTC
Forum: Forum Games
Topic: Count up with the Five Fives puzzle
Replies: 298
Views: 18047

Re: Count up with the Five Fives puzzle

61 = 55 + 5 + 5/5
Sun Jul 03, 2016 9:21 pm UTC
Forum: Forum Games
Topic: Count up with the Five Fives puzzle
Replies: 298
Views: 18047

Re: Count up with the Five Fives puzzle

44 = 55 / (5 * .5 * .5)
Sun Jul 03, 2016 1:33 am UTC
Forum: Forum Games
Topic: Count up with the Five Fives puzzle
Replies: 298
Views: 18047

Re: Count up with the Five Fives puzzle

Might as well put this new function to use.

42 = 5! * (.5/5 + .5*.5)
Fri Jul 01, 2016 10:27 pm UTC
Forum: Forum Games
Topic: Count up with the Five Fives puzzle
Replies: 298
Views: 18047

Re: Count up with the Five Fives puzzle

39 = (5 * 5 - 5.5) / .5
Wed Jun 29, 2016 5:06 am UTC
Forum: Forum Games
Topic: Count up with the Five Fives puzzle
Replies: 298
Views: 18047

Re: Count up with the Five Fives puzzle

35 = 55 + 5 - 5*5
Sun Jun 26, 2016 3:48 am UTC
Forum: Forum Games
Topic: Count up with the Five Fives puzzle
Replies: 298
Views: 18047

Re: Count up with the Five Fives puzzle

33 = 55 * (.5 + .5/5)
Sat Jun 04, 2016 5:35 am UTC
Forum: Mathematics
Topic: distance between two vertices in a random binary tree
Replies: 1
Views: 1781

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.
Tue Mar 22, 2016 2:38 pm UTC
Forum: Mathematics
Topic: Colliding Missles
Replies: 11
Views: 3185

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.
Sun Feb 28, 2016 6:10 am UTC
Forum: Forum Games
Topic: Count Up in Balanced Base 5
Replies: 43
Views: 2645

Re: Count Up in Balanced Base 5

222
Sat Feb 27, 2016 5:19 am UTC
Forum: Forum Games
Topic: Count Up in Balanced Base 5
Replies: 43
Views: 2645

Re: Count Up in Balanced Base 5

220
Fri Feb 26, 2016 9:17 pm UTC
Forum: Forum Games
Topic: Count Up in Balanced Base 5
Replies: 43
Views: 2645

Re: Count Up in Balanced Base 5

222
Thu Feb 25, 2016 8:45 pm UTC
Forum: Forum Games
Topic: Count Up in Balanced Base 5
Replies: 43
Views: 2645

Re: Count Up in Balanced Base 5

112
Tue Feb 09, 2016 9:27 pm UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 81519

Re: Count Up with the Four Fours Puzzle

490 = (((√!4)!)!! + !√4) * (4!! + √4)
Sun Feb 07, 2016 7:51 am UTC
Forum: Forum Games
Topic: My Number Is Not Your Number!
Replies: 168
Views: 16294

Re: My Number Is Not Your Number!

-12345.6789

The previous number was an integer, and this is not. Thus, they are different.
Sat Feb 06, 2016 11:11 pm UTC
Forum: Mathematics
Topic: Coin flip problem
Replies: 6
Views: 1500

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...
Fri Feb 05, 2016 9:57 pm UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 81519

Re: Count Up with the Four Fours Puzzle

486 = √4 * !4!√4/.4
Mon Jan 18, 2016 9:13 am UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 81519

Re: Count Up with the Four Fours Puzzle

301 = !(4 + √4) + (4 * !4)
Mon Jan 18, 2016 8:21 am UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 81519

Re: Count Up with the Four Fours Puzzle

299 = (4! - !√4) * (!4 + 4)
Sun Jan 17, 2016 11:43 pm UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 81519

Re: Count Up with the Four Fours Puzzle

297 = !4 * 4! + √!44
Sun Jan 17, 2016 7:28 pm UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 81519

Re: Count Up with the Four Fours Puzzle

293 = (!4 + 4!!)√4 + 4
Sat Jan 16, 2016 7:20 pm UTC
Forum: Logic Puzzles
Topic: Defective Circuit Board Puzzle
Replies: 7
Views: 2577

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...
Fri Jan 15, 2016 12:08 am UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 81519

Re: Count Up with the Four Fours Puzzle

289 = (4!! + !4) * (4!! + !4)
Thu Jan 14, 2016 9:40 pm UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 81519

Re: Count Up with the Four Fours Puzzle

287 = √!4 * (!4 - √4)! - !(4!!) = 15120 - 14833
Thu Jan 14, 2016 12:43 am UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 81519

Re: Count Up with the Four Fours Puzzle

281 = (!4)!/4! - !(4!!) - (√!4)!
Wed Jan 13, 2016 7:42 pm UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 81519

Re: Count Up with the Four Fours Puzzle

277 = 44 + 4! - √!4
Wed Jan 13, 2016 2:41 am UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 81519

Re: Count Up with the Four Fours Puzzle

270 = !4 * √(4! + !√4) * (√!4)!
Tue Jan 12, 2016 8:31 pm UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 81519

Re: Count Up with the Four Fours Puzzle

266 = !(4+√4) + 4/4
Sun Jan 10, 2016 7:05 am UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 81519

Re: Count Up with the Four Fours Puzzle

249 = 4! * (4!! + √4) + !4
Sat Jan 09, 2016 8:00 am UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 81519

Re: Count Up with the Four Fours Puzzle

247 = (!4)(!√4)/.4 + 4
Fri Jan 08, 2016 8:48 am UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 81519

Re: Count Up with the Four Fours Puzzle

241 = (4!!)!! + !√4 - 4! * (√!4)!
Fri Jan 08, 2016 4:37 am UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 81519

Re: Count Up with the Four Fours Puzzle

239 = 4! * (4!! + √4) - !√4
Thu Jan 07, 2016 7:03 am UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 81519

Re: Count Up with the Four Fours Puzzle

237 = √!4 * ((!4)√4 - √4)
Wed Jan 06, 2016 10:33 pm UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 81519

Re: Count Up with the Four Fours Puzzle

235 = √!44!!-√!4 - 4!!
Wed Jan 06, 2016 8:14 am UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 81519

Re: Count Up with the Four Fours Puzzle

226 = 4!! * (4! + 4) + √4
Wed Jan 06, 2016 4:40 am UTC
Forum: Forum Games
Topic: Count Up with the Four Fours Puzzle
Replies: 2066
Views: 81519

Re: Count Up with the Four Fours Puzzle

224 = 4 * (4√!4 - 4!!)