Search found 54 matches

by balr
Fri Oct 24, 2014 4:46 pm UTC
Forum: Logic Puzzles
Topic: Two guards, two doors, no instructions
Replies: 63
Views: 15592

Re: Two guards, two doors, no instructions

I think I am just echoing Qaanol's point here: Xenomortis: what is to stop the untruthful guard saying: "If you ask me the set up, I'd say "chose any door, both lead to freedom." Of course, if you did ask that guard, they'd give you a completely different answer, so they have ...
by balr
Thu Oct 23, 2014 10:20 am UTC
Forum: Logic Puzzles
Topic: Two guards, two doors, no instructions
Replies: 63
Views: 15592

Two guards, two doors, no instructions

The basic set up is familiar: Two guards guard two doors. One door leads to freedom, one door leads to death. You can ask one question. One guard always lies, one always tells the truth. But you know none of that....Perhaps the sign explaining it has been stolen. Before you ask your question, the gu...
by balr
Mon Sep 29, 2014 8:09 am UTC
Forum: Logic Puzzles
Topic: Simple grid placement puzzle
Replies: 12
Views: 3265

Re: Simple grid placement puzzle

Nice analysis!

I think we have a winner.
by balr
Sat Sep 27, 2014 9:55 am UTC
Forum: Logic Puzzles
Topic: Simple grid placement puzzle
Replies: 12
Views: 3265

Re: Simple grid placement puzzle

That looks good, lunch meat . I think we followed similar logic paths to get there: 2 has to go on a middle edge (not corner), so we can start with: ? 2 ? ? ? ? ? ? ? ? ? ? ? ? ? ? (in your case, you started with the bottom row. Same difference). If we are aiming for the lowest solut...
by balr
Thu Sep 25, 2014 8:51 am UTC
Forum: Logic Puzzles
Topic: Simple grid placement puzzle
Replies: 12
Views: 3265

Re: Simple grid placement puzzle

That didn't last long! curiosityspoon and nitrodon have both pretty much replicated the analysis I made to solve the puzzle, so I won't bother publishing that. Now 4x4 with the same rules is a bit tougher to find a solution - there are quite a few. Can you find one of them? How about the lowest solu...
by balr
Wed Sep 24, 2014 4:33 pm UTC
Forum: Logic Puzzles
Topic: Simple grid placement puzzle
Replies: 12
Views: 3265

Simple grid placement puzzle

The challenge: Place the digits 1 through 9 into a 3x3 grid subject to two constraints: 1. No numbers that exactly divide each other can be in the same row, column, or long diagonal (1 doesn't count as a divisor for this puzzle) 2. No numbers that are +/-1 of each other can be adjacent vertically o...
by balr
Thu May 09, 2013 1:30 pm UTC
Forum: Logic Puzzles
Topic: Team challenge
Replies: 22
Views: 8282

Re: Team challenge

It can't be done, except in the degenerate case where sets of three people have (by random choice) all picked each other. In that case, A, B, and C can be equidistant from each other, independently of D, E and F being a different equidistance, and so on. But four people cannot be equidistant from ea...
by balr
Mon Feb 11, 2013 10:48 am UTC
Forum: Logic Puzzles
Topic: Tea or Coffee
Replies: 13
Views: 6141

Re: Tea or Coffee

The answer above works for a perfect spoon - i.e. one that is completely dry at the end of each transfer. A real spoon will be wet, thus abstracting a small quantity of the fluid(s) at the end of the two transfers. We need to know the amount and proportions of the two fluids in each of the three loc...
by balr
Fri Feb 01, 2013 12:39 pm UTC
Forum: Logic Puzzles
Topic: Pennies in Boxes
Replies: 85
Views: 50277

Re: Pennies in Boxes

Sell the boxes intact for USD5 each. Offer a prize of USD1000 for anyone who has purchased two that are identical. (You'll need to put some sort of buyer-id mark on them to stop box buyers swapping boxes between themselves after purchase). If your initial sample result (that no boxes two seem alike)...
by balr
Fri Feb 01, 2013 12:20 pm UTC
Forum: Logic Puzzles
Topic: The truthteller and the politician
Replies: 65
Views: 25401

Re: The truthteller and the politician

Spoiler:
Do you want people to vote for you at the next election?


A truthteller would simply say no. A politician could say no, but they'd be committing career suicide, so they'd be left waffling in the wind.

Alternatively:
Spoiler:
Do you do a good job in representing your constituents?
by balr
Sun Sep 09, 2012 11:05 am UTC
Forum: Logic Puzzles
Topic: Pennies in Boxes
Replies: 85
Views: 50277

Re: Pennies in Boxes

One word: Crowdscourcing. Get other people do do the work for you, and have them pay you do it it. Rent access to the box at (say) USD5 per hour. Let the extractors take whatever cardboard and pennies they can extract. Sell them knives, coffee, charge for bathroom access, charge high rates f...
by balr
Tue Mar 13, 2012 7:19 pm UTC
Forum: Logic Puzzles
Topic: Problem with Carpooling
Replies: 26
Views: 10153

Re: Problem with Carpooling

Some further issues regarding car pool fairness. 1. With an irregular group of carpoolers (as stated in the original spec) there may be days where more than a carful want a ride. There'd be two (or more) drivers that day. 2. The workload for a driver is (loosely) correlated with the number of riders...
by balr
Fri Nov 25, 2011 6:32 pm UTC
Forum: Logic Puzzles
Topic: Help crack the code plzz ......
Replies: 2
Views: 1706

Re: Help crack the code plzz ......

Looks like a SHA1 digest.

If so all you have to do to win is
Spoiler:
guess the word or phrase Ted has encoded. It probably includes the string TalkMagic.
by balr
Tue Nov 22, 2011 2:35 pm UTC
Forum: Logic Puzzles
Topic: 2 + 2 = 5
Replies: 175
Views: 52813

Re: 2 + 2 = 5

But what if there are holes in the number line, and the first hole turns out (on closer inspection) to be where we've always assumed 4 to be? This is explored in Rudy Rucker 's short story, 2 + 2 = 5 http://kasmana.people.cofc.edu/MATHFICT/mfview.php?callnumber=mf589 (Even if it unlikely that 4 is l...
by balr
Tue Oct 18, 2011 5:29 pm UTC
Forum: Logic Puzzles
Topic: Algebra Crypotgram Puzzle
Replies: 13
Views: 4574

Re: Algebra Crypotgram Puzzle

Wow -- that old programmer's joke has catalyzed a lot of multi-base alphameric research. Thanks for sharing the findings.

Here's a simple looking alphametic equation that has unique solution in every base from 5 to, well, there may be no limit -- try it for yourself:

Code: Select all

JUL + 4 = USA
by balr
Fri Oct 14, 2011 11:22 am UTC
Forum: Logic Puzzles
Topic: Algebra Crypotgram Puzzle
Replies: 13
Views: 4574

Re: Algebra Crypotgram Puzzle

Thanks for playing, solving, and confirming my suspicions about the uniqueness of the answers. Incidentally, there are three solutions in hexadecimal (base 16), and one of them is noticeably bad. You'll know what I mean if you find that solution (in the base-16 variant, C,D,E are still variables, no...
by balr
Sun Oct 09, 2011 1:10 pm UTC
Forum: Logic Puzzles
Topic: Algebra Crypotgram Puzzle
Replies: 13
Views: 4574

Re: Algebra Crypotgram Puzzle

feel free to post if you find more puzzles of this type Okay, here's one. It's based on the old joke: why do computer programmers confuse Halloween with Xmas? DEC * 25 = OCT * 31 Where, as usual, letters are difference digits, and D and O are never zero (no leading zeroes). Digits are themselves. *...
by balr
Thu Sep 29, 2011 9:41 pm UTC
Forum: Logic Puzzles
Topic: Solve this! (A mathemagical game.)
Replies: 62
Views: 10171

Re: Solve this! (A mathemagical game.)

Fair cake algorithm -- this works for a round cake with precisely vertical cuts -- it would not work if one person's idea of fairness was for them to have all the cream filling via some horizontal cuts. The solution is shown for three people, but it extends to higher numbers. First, make one arbitra...
by balr
Fri Sep 23, 2011 2:28 pm UTC
Forum: Logic Puzzles
Topic: A Syllogism by Lewis Carroll
Replies: 11
Views: 5345

Re: A Syllogism by Lewis Carroll

What seems to be missing is a qualification: All meat that I eat for dinner is meat that I buy at the market. All meat that I buy at the market was raw meat at the time of purchase Therefore: All meat that I eat for dinner was raw meat at the time of purchase Consider an equivalent syllogism: All pe...
by balr
Wed Sep 14, 2011 3:12 pm UTC
Forum: Logic Puzzles
Topic: Interesting Math/Logic Puzzle
Replies: 4
Views: 2118

Re: Interesting Math/Logic Puzzle

I wrote a very short REBOL script:
Spoiler:

Code: Select all

start: 1-August-1948
loop 10 [print start: start - 1000]

5-Nov-1945
9-Feb-1943
15-May-1940
19-Aug-1937
23-Nov-1934
27-Feb-1932
2-Jun-1929
6-Sep-1926
11-Dec-1923
16-Mar-1921
by balr
Wed Sep 14, 2011 3:56 am UTC
Forum: Logic Puzzles
Topic: Interesting Math/Logic Puzzle
Replies: 4
Views: 2118

Re: Interesting Math/Logic Puzzle

Spoiler:
1926
by balr
Fri Sep 09, 2011 1:35 pm UTC
Forum: Logic Puzzles
Topic: Chess problem I just invented; can't solve
Replies: 11
Views: 3696

Re: Chess problem I just invented; can't solve

This can be done,sort of, in a match of two or more games white starts a new game 1. Nf3 Nf6 2. Ng1 Ng8 3. Nf3 Nf6 4. Ng1 Ng8 = draw by repetition It is now the original Black player's turn to move to start the next game. Admittedly, they'll move with the White pieces, but they were Black so...
by balr
Mon Aug 01, 2011 8:43 am UTC
Forum: Logic Puzzles
Topic: An alien in need
Replies: 6
Views: 2732

Re: An alien in need

Eternal Questionner wrote:Left to right's 50:50 anyway


Not quite - you are overlooking Boustrophedon writing.
by balr
Tue Jun 28, 2011 3:11 pm UTC
Forum: Logic Puzzles
Topic: Numbers and Squares
Replies: 16
Views: 4228

Re: Numbers and Squares

Here's an answer that squeezes the facts until they fit, and produces the same end result as GeorgeH. Add all corner numbers that are either prime or one less than a prime. The in-box number is that total expressed in base 17 8 + 4 + 9 + 2 ===> 4 + 2 = 6 2 + 17 + 6 + 10 ===> 2 + 17 + 6 + 10 = 35 ...
by balr
Fri Jun 03, 2011 12:14 pm UTC
Forum: Logic Puzzles
Topic: Longest english contraction
Replies: 21
Views: 41573

Re: Longest english contraction

How is this scored? Most apostrophes wins, with letter count as a tiebreaker?


Good question!

That sounds a fine scheme.
by balr
Fri Jun 03, 2011 9:47 am UTC
Forum: Logic Puzzles
Topic: Longest english contraction
Replies: 21
Views: 41573

Longest english contraction

Someone asked this on the Stack Exchange English site, and it got closed as unsuitable for a language site. Perhaps it'll fare better in a logic puzzle forum. The puzzle is (as expressed by the original poster) to find the: largest word with multiple contractions . Their offering is .... The fish...
by balr
Sat May 14, 2011 10:19 am UTC
Forum: Logic Puzzles
Topic: Twins in a Maze
Replies: 81
Views: 20305

Re: Twins in a Maze

If we're on a featureless sphere orbiting a featureless star, then I'd fly to the L2 Lagrange point -- as would my twin robot; after we've used our unlimited time to develop space flight...If I can see the sky, then it's part of the maze by the original definition, that that's a logi...
by balr
Wed May 11, 2011 1:26 pm UTC
Forum: Logic Puzzles
Topic: Twins in a Maze
Replies: 81
Views: 20305

Re: Twins in a Maze

I don't want to hijack this thread into a discussion on logical puzzles vs engineering puzzles … so please feel free to cut out this post and its context and park somewhere else. But many logic puzzles are also engineering puzzles. Consider, for example, the whole genre of coin piles that have to be...
by balr
Wed May 11, 2011 7:02 am UTC
Forum: Logic Puzzles
Topic: Twins in a Maze
Replies: 81
Views: 20305

Re: Twins in a Maze

But there is always going to be a symmetry breaker -- if not in the twins themselves (their names or ages as previously discussed) then in their initial position or orientation in the maze. Developing that spoiler further -- consider the example given of a perfectly circular maze and the twins dropp...
by balr
Mon Mar 07, 2011 12:24 pm UTC
Forum: Logic Puzzles
Topic: Not friends on the earth
Replies: 19
Views: 3707

Re: Not friends on the earth

So then I guess a better way would be saying "Distribute N points on a sphere surface..." rather than having them all start at the north pole Puzzles are often characterized by being expressed in a narrative form, and wrapped in a story. Some can be re-cast into a formal mathematical form...
by balr
Sun Mar 06, 2011 8:57 pm UTC
Forum: Logic Puzzles
Topic: Not friends on the earth
Replies: 19
Views: 3707

Re: Not friends on the earth

Thanks for asking for clarification.

My unstated assumptions in the original question were for
  • final distance
  • as measured on the surface (ie no tunnelling with tape measures)
So we're looking for final great circle distances.
by balr
Thu Feb 24, 2011 10:17 am UTC
Forum: Logic Puzzles
Topic: Not friends on the earth
Replies: 19
Views: 3707

Re: Not friends on the earth

Ralp.....The 2, 3, 4 solutions may not be very interesting, but I do not think there are any solutions for 5 and above. The original puzzle asks for the distances to be maximal and equal . Your suggested 5 solution has four people around the equator. They are not all the same distance from each othe...
by balr
Wed Feb 23, 2011 11:18 pm UTC
Forum: Logic Puzzles
Topic: Not friends on the earth
Replies: 19
Views: 3707

Re: Not friends on the earth

To clarify a possible misreading: everyone stays on the surface of the earth at all times.
by balr
Wed Feb 23, 2011 10:27 pm UTC
Forum: Logic Puzzles
Topic: Not friends on the earth
Replies: 19
Views: 3707

Not friends on the earth

For the purpose of these puzzles, the Earth is a uniform, smooth, sphere of circumference 40,000km. Easy to start: a. Two people who dislike each other very much stand at the North Pole. One moves to be as far away from the other person as they can. How far is that? Now, the real problems: b. Three...
by balr
Wed Feb 23, 2011 12:09 pm UTC
Forum: Logic Puzzles
Topic: Sum of consecutive integers
Replies: 10
Views: 4328

Re: Sum of consecutive integers

Thanks for the corrections.

My script emitted the right solutions, but injuries sustained during the edit wars still affect my ability to cut'n'paste properly.

Incidentally, if we permit negative integers, then even powers of 2 have a solution:
Spoiler:
-3 + -2 + -1 + 0 + 1 + 2 + 3 + 4 = 4
by balr
Wed Feb 23, 2011 10:10 am UTC
Forum: Logic Puzzles
Topic: Sum of consecutive integers
Replies: 10
Views: 4328

Re: Sum of consecutive integers

(belated reply to skyreaper....other edits and replies have outdated this while I was typing) You are on the right track with the idea you added in an edit. Incidentally, 6177 has five solutions: 2058 + 2059 + 2060 = 6177 1027 + 1028 + 1029 + 1030 + 1031 + 1032 = 6177 199 + 200 + 201 + 202 + 203 + 2...
by balr
Wed Feb 23, 2011 9:31 am UTC
Forum: Logic Puzzles
Topic: Sum of consecutive integers
Replies: 10
Views: 4328

Re: Sum of consecutive integers

That was quick!

Your suspicion is well-founded. If you can deduce the algorithm for producing the consecutive integers for a given number, you'd be able to tell if
  • your suspicion is correct
  • there are any other unreachable numbers
by balr
Wed Feb 23, 2011 8:59 am UTC
Forum: Logic Puzzles
Topic: Sum of consecutive integers
Replies: 10
Views: 4328

Sum of consecutive integers

Some numbers can be expressed as the sum of consecutive positive integers: 2 + 3 = 5 1 + 2 + 3 + 4 = 10 Some can be expressed in more than one way: 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 = 72 23 + 24 + 25 = 72 Can you find all the ways to express these integers -- or explain why it is not possible? 99...
by balr
Thu Feb 17, 2011 9:41 pm UTC
Forum: Logic Puzzles
Topic: Twins in a Maze
Replies: 81
Views: 20305

Re: Twins in a Maze

The problem states: You and your twin know that, being identical in mind and body, each will arrive at the same method as the other Therefore we will both arrive at the same method, X . For us to succeed we must break the symmetry, and have one of us implement it as X while the other implements it a...
by balr
Sun Feb 06, 2011 7:16 pm UTC
Forum: Logic Puzzles
Topic: Twins in a Maze
Replies: 81
Views: 20305

Re: Twins in a Maze

The original rules state that: You cannot call out to one another, leave markings or a trail. So shouting is ruled out. But it is physically impossible, given the problem states that the twins are human, (the problem is posed for You and your identical twin ) not to leave a trail. Again, the problem...

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