Search found 224 matches

by sfwc
Wed Jun 14, 2017 9:47 am UTC
Forum: Logic Puzzles
Topic: Guess the Pattern
Replies: 21
Views: 3474

Re: Guess the Pattern

A further observation, which narrows things down quite a lot: The output for n is always a prime p such that n + p is also prime. Furthermore, the output is almost always the smallest prime p such that n+p is prime, with the exceptions being at 90, 1002, 1080, 10^6 + 1, 10^6 + 12, 10^6 + 20, 10^6 + ...
by sfwc
Thu Apr 06, 2017 7:19 pm UTC
Forum: Logic Puzzles
Topic: Pirate Game - A Variation [solutions]
Replies: 0
Views: 2194

Pirate Game - A Variation [solutions]

Original thread To help distinguish them grammatically, I’m assuming that pirates A, C and E are male but pirates B and D are female. For a given pirate p, I’ll use the phrase `scenario p’ to describe what would happen if, in the final voting, pirate p (and therefore also all pirates of higher rank...
by sfwc
Wed Mar 29, 2017 3:51 pm UTC
Forum: Logic Puzzles
Topic: Two secrets
Replies: 20
Views: 4844

Re: Two secrets

This method gets the number of questions down to a constant multiple of log(N)^4: The plan is to find a collection of subsets such that, for any 4 distinct numbers (a,b,c,d) in 1…N at least one of the sets contains both a and b but neither c nor d. After asking about each of these sets we’ll...
by sfwc
Mon Nov 21, 2016 11:01 am UTC
Forum: Logic Puzzles
Topic: Hidden Cards
Replies: 5
Views: 2783

Re: Hidden Cards

It makes sense for the logicians to at least follow this rule: if you know that you can guess correctly, then raise your hand immediately. Otherwise, wait a little to give those who can guess correctly a chance, and then raise your hand a little later if nobody else does (the time you wait should be...
by sfwc
Mon Jan 25, 2016 10:56 am UTC
Forum: Logic Puzzles
Topic: Defective Circuit Board Puzzle
Replies: 7
Views: 2375

Re: Defective Circuit Board Puzzle

Jestingrabbit's solution is indeed optimal. Here is a proof: Jestingrabbit gave a method to identify the bad boards within 6 trials. So we have to show that there is no method which will allow us to consistently identify the bad boards within five trials. On any given trial the machine will identify...
by sfwc
Wed May 20, 2015 3:48 pm UTC
Forum: Logic Puzzles
Topic: Tricky geometric proof
Replies: 8
Views: 5152

Re: Tricky geometric proof

Let K be the intersection of AC and BD. Note that AC and BD meet at right angles because ABD = DBC and BA = BC. We have ACF = KCB = 90 - KBC = 90 - DBE = BDE and CFA = 90 = DEB, so that the triangles ACF and BDE are similar. Let K' be the intersection of GE and BD. Then ABC = GBE and ACB = KCB ...
by sfwc
Fri May 15, 2015 12:32 pm UTC
Forum: Logic Puzzles
Topic: Some word puzzle i found - Solved
Replies: 2
Views: 1639

Re: Some word puzzle i found

Spoiler:
The number of letters is 25, a square number, so arrange the letters in a square and then read down the columns rather than along the rows:

Code: Select all

HWTAS
EAHSN
YSEYT
IRRWI
TAEAT
by sfwc
Fri Dec 06, 2013 4:17 pm UTC
Forum: Logic Puzzles
Topic: Find a set of numbers containing mine
Replies: 32
Views: 9450

Re: Find a set of numbers containing mine

I came up with a similar solution (though my explanation has more waffle and the way I go from 1023 down to 512 is different). First, I'll explain how Bob can achieve a slightly easier task, namely finding a set of 1023 numbers at least one of which must be Alice's. Bob keeps track of a set ...
by sfwc
Sat Nov 30, 2013 3:12 pm UTC
Forum: Logic Puzzles
Topic: Misplaced Christmas presents
Replies: 11
Views: 5361

Re: Misplaced Christmas presents

A complete description of all solutions: The only solution is 2, 3, 7. Let A, B, C be a solution. As already noted, A, B and C must be coprime integers, and all must be at least 2. Also, AB + 1 is a multiple of C, BC + 1 is a multiple of A and AC + 1 is a multiple of B. So AB + BC + AC + 1 is a mult...
by sfwc
Tue Jul 09, 2013 6:03 pm UTC
Forum: Logic Puzzles
Topic: Hats
Replies: 42
Views: 13646

Re: Hats

I think I have now resolved this question in the case that there is some finite number n of available colours, for an arbitrary number p of people. The solution is that the prisoners cannot guarantee that even one of them will name the colour of their own hat if the number of rats is at least the in...
by sfwc
Thu Jun 20, 2013 5:31 pm UTC
Forum: Logic Puzzles
Topic: Hats
Replies: 42
Views: 13646

Re: Hats

I think I can solve the problem with 50 rats and two colours. More precisely, since there have been a number of variants proposed, I think I can solve the following: 100 people are in a line They have 1 or 0 hat color (yes those ARE colors thank you very much) They don't know their hat color They ca...
by sfwc
Mon Feb 18, 2013 9:49 pm UTC
Forum: Fit Club
Topic: Run 10,000 miles
Replies: 1340
Views: 259108

Re: Run 10,000 miles

9872 + 3.9 = 9875.9
by sfwc
Fri Feb 15, 2013 9:22 am UTC
Forum: Fit Club
Topic: Run 10,000 miles
Replies: 1340
Views: 259108

Re: Run 10,000 miles

9853.1 + 5.8 = 9858.9
by sfwc
Mon Feb 11, 2013 5:16 pm UTC
Forum: Fit Club
Topic: Run 10,000 miles
Replies: 1340
Views: 259108

Re: Run 10,000 miles

9800 + 4.1 = 9804.1
by sfwc
Thu Feb 07, 2013 8:44 pm UTC
Forum: Fit Club
Topic: Run 10,000 miles
Replies: 1340
Views: 259108

Re: Run 10,000 miles

9779.4 + 3.5 + 5.8 + 8 = 9796.7
by sfwc
Sun Feb 03, 2013 5:20 pm UTC
Forum: Fit Club
Topic: Run 10,000 miles
Replies: 1340
Views: 259108

Re: Run 10,000 miles

9737.2 + 8 = 9745.2
by sfwc
Thu Jan 31, 2013 8:32 pm UTC
Forum: Fit Club
Topic: Run 10,000 miles
Replies: 1340
Views: 259108

Re: Run 10,000 miles

9714.8 + 5.8 = 9720.6
by sfwc
Thu Jan 24, 2013 4:47 pm UTC
Forum: Fit Club
Topic: Run 10,000 miles
Replies: 1340
Views: 259108

Re: Run 10,000 miles

9649.4 + 5.8 + 8 = 9663.2
by sfwc
Sat Jan 19, 2013 9:55 pm UTC
Forum: Fit Club
Topic: Run 10,000 miles
Replies: 1340
Views: 259108

Re: Run 10,000 miles

9610.6 + 3.3 + 6.3 = 9620.2
by sfwc
Wed Jan 02, 2013 9:16 pm UTC
Forum: Fit Club
Topic: Run 10,000 miles
Replies: 1340
Views: 259108

Re: Run 10,000 miles

9580.5 + 4.9 = 9585.4
by sfwc
Tue Dec 18, 2012 10:33 am UTC
Forum: Fit Club
Topic: Run 10,000 miles
Replies: 1340
Views: 259108

Re: Run 10,000 miles

9554.4 + 4 = 9558.4
by sfwc
Sat Dec 15, 2012 10:41 pm UTC
Forum: Fit Club
Topic: Run 10,000 miles
Replies: 1340
Views: 259108

Re: Run 10,000 miles

9549.3 + 2 = 9551.3
by sfwc
Thu Dec 13, 2012 9:41 pm UTC
Forum: Fit Club
Topic: Run 10,000 miles
Replies: 1340
Views: 259108

Re: Run 10,000 miles

9540.3 + 5.8 = 9546.1
by sfwc
Tue Dec 11, 2012 9:58 am UTC
Forum: Logic Puzzles
Topic: Squish the bug
Replies: 20
Views: 4573

Re: Squish the bug

dudiobugtron wrote:What is the integer part of 1.99999999999999..... ?

I'll leave that for those more learned than me to discuss. Somewhere else, preferably.
by sfwc
Mon Dec 10, 2012 5:33 pm UTC
Forum: Logic Puzzles
Topic: Squish the bug
Replies: 20
Views: 4573

Re: Squish the bug

Yes, we can still squish the bug. First, I'll make the problem more precise: we have to find a sequence (k i ) of integers with the following property: for any real numbers x and y there is some i such that the integer part of x + i*y is k i . I'm using `integer part' rather than...
by sfwc
Sun Dec 09, 2012 9:04 pm UTC
Forum: Fit Club
Topic: Run 10,000 miles
Replies: 1340
Views: 259108

Re: Run 10,000 miles

9506.1 + 5.8 = 9511.9

Sorry I've not been running for a bit - I hurt my knee (it is almost back to normal now).
by sfwc
Thu Nov 22, 2012 4:54 pm UTC
Forum: Logic Puzzles
Topic: Blocking game
Replies: 8
Views: 2996

Re: Blocking game

You appear to be making the stronger claim that the blocking game on a single board will never end. In fact, the blocker always has a winning strategy, whether they play first or second (you missed some `2-moves-to-victory' possibilities). Here is a winning strategy: First, get all 3 blocking pieces...
by sfwc
Thu Nov 15, 2012 6:42 pm UTC
Forum: Fit Club
Topic: Run 10,000 miles
Replies: 1340
Views: 259108

Re: Run 10,000 miles

9220.5 + 5.8 = 9226.3
by sfwc
Sun Nov 11, 2012 9:34 pm UTC
Forum: Fit Club
Topic: Run 10,000 miles
Replies: 1340
Views: 259108

Re: Run 10,000 miles

9203.1 + 7.9 = 9211
by sfwc
Thu Nov 08, 2012 4:52 pm UTC
Forum: Fit Club
Topic: Run 10,000 miles
Replies: 1340
Views: 259108

Re: Run 10,000 miles

9180 + 4 + 5.8 = 9189.8
by sfwc
Tue Oct 30, 2012 8:21 am UTC
Forum: Fit Club
Topic: Run 10,000 miles
Replies: 1340
Views: 259108

Re: Run 10,000 miles

9151.6 + 4.3 + 5.8 + 8 = 9169.7
by sfwc
Sat Oct 27, 2012 5:35 pm UTC
Forum: Fit Club
Topic: Run 10,000 miles
Replies: 1340
Views: 259108

Re: Run 10,000 miles

9125 + 7.9 = 9132.9
by sfwc
Wed Oct 24, 2012 10:57 am UTC
Forum: Fit Club
Topic: Run 10,000 miles
Replies: 1340
Views: 259108

Re: Run 10,000 miles

9109.5 + 4.2 + 5.8 = 9119.5
by sfwc
Sun Oct 21, 2012 5:01 pm UTC
Forum: Fit Club
Topic: Run 10,000 miles
Replies: 1340
Views: 259108

Re: Run 10,000 miles

9082.8 + 8 = 9090.8
by sfwc
Fri Oct 19, 2012 4:06 pm UTC
Forum: Fit Club
Topic: Run 10,000 miles
Replies: 1340
Views: 259108

Re: Run 10,000 miles

9070.3 + 4 = 9074.3
by sfwc
Tue Oct 16, 2012 7:34 am UTC
Forum: Fit Club
Topic: Run 10,000 miles
Replies: 1340
Views: 259108

Re: Run 10,000 miles

9041.8 + 4.4 = 9046.2
by sfwc
Sat Oct 13, 2012 11:50 am UTC
Forum: Fit Club
Topic: Run 10,000 miles
Replies: 1340
Views: 259108

Re: Run 10,000 miles

That doesn't look right. I'll assume that the figure 223.5 is the correct one rather than 9199, so I get the following:

8752.0 + 223.5 = 8975.5

Now I'll add my own run:

8975.5 + 8.1 = 8983.6
by sfwc
Thu Oct 11, 2012 3:56 pm UTC
Forum: Fit Club
Topic: Run 10,000 miles
Replies: 1340
Views: 259108

Re: Run 10,000 miles

8473.9 + 5.8 = 8479.7
by sfwc
Wed Oct 10, 2012 12:57 pm UTC
Forum: Logic Puzzles
Topic: Tantrix
Replies: 8
Views: 2410

Re: Tantrix

I have no idea how you're supposed to solve these without just using trial and error... I'm sure if I just kept trying patterns I'd eventually found one that fit, but that's not particularly satisfying... I have a pen-and-paper method, but it is complicated (hence the repeated mistakes). However, h...
by sfwc
Tue Oct 09, 2012 11:34 am UTC
Forum: Logic Puzzles
Topic: Tantrix
Replies: 8
Views: 2410

Re: Tantrix

newbie11 wrote:Sorry, that is incorrect. Good try though!

Ooops! I'll have another go:
Spoiler:
A = 5, B = 7, C = 9, D = 2, E = 1, F = 3

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