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Topic: Mind Games (Read 2008 times) |
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rmsgrey
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A series, called Mind Games, on digital TV here in UK (Monday, 9pm, BBC4) I discovered this evening which basicaly consists of two teamsof two solving riddles turned up these two:
1) A circular bar mat, with a design that could be generated by drawing a circle concentric with the mat and radius roughly 3/4 of the mat's, then dividing the space outside the circle into 8 equal regions with 8 radial lines to produce a highly symmetric pattern (8-fold reflectional symmetry). Each of the 8 outer sections has a letter in, written using a seven-segment LED display style font (think calculator display). The letters are AHPLLCII (to avoid ambiguity, the I's use the two left-hand segments) and are arranged in that order reading clockwise so that the hypothetical 7-segment displays wouldn't break the symmetry of the wheel.
The challenge is to cut the mat with as few continuous cuts (not necessarily straight) as possible and then rearrange the pieces to give the two words CLIP and HAIL. A cut ends as soon as it intersects either the edge of the mat or a previous cut, or itself.
2) What is the next number in the following sequence:
2, 4, 6, 30, 32, 34, 36, 40, 42, 44, 46, 50, 52, 54, 56, 60, 62, 64, 66, ...
(It's less than one billion)
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John_Gaughan
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Re: Mind Games
« Reply #1 on: Oct 26th, 2004, 6:29am » |
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1) I suspect that the ideal solution involves cutting pieces that are larger than one letter and turning them upside down, e.g. using IAH as one cut and flipping it over to make HAI. This only works for this run, however, so the others probably need more cuts. I say four cuts are necessary.
2) 70 is wrong, because it is too obvious  I have no idea what the correct answer might be.
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Grimbal
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Re: Mind Games
« Reply #2 on: Oct 26th, 2004, 7:17am » |
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on Oct 26th, 2004, 6:29am, John_Gaughan wrote:| 2) 70 is wrong, because it is too obvious I have no idea what the correct answer might be. |
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And it does not explain why the 10's and 20's were skipped.
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rmsgrey
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Re: Mind Games
« Reply #3 on: Oct 26th, 2004, 9:14am » |
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To clarify, the mat is only printed on one side. Short of using a fourth dimension, I can't see a way to transform IAH to HAI - you end up with H[funny shape like a half-full glass]I (and the I ends up right-justified rather than left-justified, but that's allowable)
The numerical sequence given is all the integers greater than 0 and less than 70 (and, yes, that isn't the answer)
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John_Gaughan
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Re: Mind Games
« Reply #4 on: Oct 26th, 2004, 11:11am » |
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1) Does the final product have to be a circle/wheel, or can I cut letters out and spell the words in a line? Also, do the words have to be separate, or can they run together as in HAILCLIP or CLIPHAIL?
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Emul P Edmon
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Re: Mind Games
« Reply #5 on: Oct 26th, 2004, 11:49am » |
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 I can do the first one in a single cut. Answer (in reverse) [smiley=longrightarrow.gif] .noitator a fo htgie eno esiwkcolcretnuoc elcric edistuo eht etator neht srettel eht hguorht yaw flah fo edisni tsuj elcric a tuC
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| « Last Edit: Oct 26th, 2004, 11:50am by Emul P Edmon » |
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rmsgrey
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Re: Mind Games
« Reply #6 on: Oct 26th, 2004, 12:32pm » |
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on Oct 26th, 2004, 11:11am, John_Gaughan wrote:| 1) Does the final product have to be a circle/wheel, or can I cut letters out and spell the words in a line? Also, do the words have to be separate, or can they run together as in HAILCLIP or CLIPHAIL? |
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The contestants got one point (of a possible two) for cutting all the letters out individually, and arranging them like a surreal ransom note.
As long as the two words don't interpenetrate, it doesn't matter where they are in relation to each other.
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rmsgrey
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Re: Mind Games
« Reply #7 on: Oct 26th, 2004, 12:36pm » |
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on Oct 26th, 2004, 11:49am, Emul P Edmon wrote:| I can do the first one in a single cut. |
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Yep, apart from having it all backwards, that's exactly right
[e]Oh, and you missed an 'h' in "hthgie", but since it took me three tries to notice that, it hardly matters [/e]
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| « Last Edit: Oct 26th, 2004, 2:53pm by rmsgrey » |
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John_Gaughan
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Re: Mind Games
« Reply #8 on: Oct 26th, 2004, 1:49pm » |
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The backwards answer is really good. I guess the part about cutting the seven LED pieces went over my head 
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rmsgrey
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Re: Mind Games
« Reply #9 on: Oct 26th, 2004, 2:58pm » |
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on Oct 26th, 2004, 1:49pm, John_Gaughan wrote:| The backwards answer is really good. I guess the part about cutting the seven LED pieces went over my head |
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I was still fumbling with completely hopelessly wrong ideas when the show's host gave the answer myself.
Any progress on the sequence?
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Emul P Edmon
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Re: Mind Games
« Reply #10 on: Oct 26th, 2004, 3:23pm » |
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I gave up and searched the web for the answer to number two. It seems to be a common puzzle and the answer is embarrassingly simple. I won't spoil it by telling anyone.
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John_Gaughan
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Re: Mind Games
« Reply #11 on: Oct 27th, 2004, 8:28am » |
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on Oct 25th, 2004, 4:43pm, rmsgrey wrote:2) What is the next number in the following sequence:
2, 4, 6, 30, 32, 34, 36, 40, 42, 44, 46, 50, 52, 54, 56, 60, 62, 64, 66, ...
(It's less than one billion) |
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This is neither arithmatic nor geometric, so I started looking at linguistics... length of the number spelled out in English... "loops" in the numerals... letters used...
:: 2,000 ::
Mathworld confirms my guess! Yay! I finally got one of these language number problems correct!
For more information :: the specific series involved is the Eban Number series, in which the numbers, when spelled out in English, do not contain the letter "e" anywhere ::
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rmsgrey
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Re: Mind Games
« Reply #12 on: Nov 2nd, 2004, 8:39am » |
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Just one that I can remember from this week's show:
3) There is a birthday cake with 7 candles. The aim is to extinguish all the candles in as few puffs as possible. Each puff will affect precisely 3 (no fewer, no more) consecutive candles (around the edge of the circular cake), blowing out any of the three that are lit, and (strangely) reigniting any unlit candles.
And another one from the previous show:
4) Three identical triplets, celebrating coming of age to drink, go to their local bar and order a large quantity of drinks. When it comes time to share the last round evenly between them, they find themselves with 7 pints, 7 half-pints, and 7 empty glasses. Without any further measuring devices (and given that the glasses, while all capable of holding a pint, are non-identical and have no markings) how can they divide the glasses and liquid between them so that each of them gets the same number of full pints, half pints and empty glasses?
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coolnfundu
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Re: Mind Games
« Reply #13 on: Nov 2nd, 2004, 8:39pm » |
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well how about doing this blow off four candles
Light the first or fourth candle again, position yourself such that you blow from first or fourth candle to extinguish others in the second puff possible ...
But I suspect, you meant we cant light the candles again ...
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Grimbal
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Re: Mind Games
« Reply #14 on: Nov 3rd, 2004, 1:51am » |
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4)
A: 3 full 3 empty 1 half
B: 3 full 3 empty 1 half
C: 1 full 1 empty 5 half
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Grimbal
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Re: Mind Games
« Reply #15 on: Nov 3rd, 2004, 1:59am » |
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3) >>go around the cake and blow each possible group of 3 once. Needs 7 puffs.<<
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| « Last Edit: Nov 3rd, 2004, 2:00am by Grimbal » |
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rmsgrey
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Re: Mind Games
« Reply #16 on: Nov 3rd, 2004, 8:56am » |
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on Nov 2nd, 2004, 8:39am, rmsgrey wrote:| each of them gets the same number of full pints, half pints and empty glasses? |
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Sorry Grimbal, but your solution isn't quite there - the amount of alcohol each isthe same, but it's divided differently...
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towr
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Re: Mind Games
« Reply #17 on: Nov 3rd, 2004, 9:38am » |
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4) ::take 4 of the half pints, add two of them to the other two, which gives two full pints and two empty glasses
So there's now 9 full, 3 half full, and 9 empty. Easy enough to divide equally::
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Emul P Edmon
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Re: Mind Games
« Reply #18 on: Nov 3rd, 2004, 4:51pm » |
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3) :: Start anywhere, go sequentially around the cake 3 full times (7 blows), hitting each candle 3 times (out, lit, then out again) so they are all out. i.e. (1, 2, 3) then (4, 5, 6) then (7, 1, 2) then (3, 4, 5) then (6, 7, 1) then (2, 3, 4) then (5, 6, 7). Naw, there's gotta be a way to do it in less tries. :: 
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| « Last Edit: Nov 3rd, 2004, 4:52pm by Emul P Edmon » |
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coolnfundu
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Re: Mind Games
« Reply #19 on: Nov 3rd, 2004, 8:48pm » |
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on Nov 2nd, 2004, 8:39am, rmsgrey wrote:
There is a birthday cake with 7 candles. The aim is to extinguish all the candles in as few puffs as possible. Each puff will affect precisely 3 (no fewer, no more) consecutive candles (around the edge of the circular cake), blowing out any of the three that are lit, and (strangely) reigniting any unlit candles.
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Ok so he says 3 consectuve ones are blown off at a time but cant that be interpreted to read that hit any candle with a puff (provided all are lit) and three consecutive cnadles on either side (ccw as well as cw) would then extinguish.
I mean lets say we have candles 1,2,3,4,5,6,7 and now I hit 4 with a puff 1,2,3 are consecutive near to 4 (say cw) as well as 5,6,7 are consecutive near to 4 as well (saw ccw). Or is there a algorithm at work that only ccw or cw candles are blown off (or lit)? If not, then one puff is the perfectly logical answer I would say.
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towr
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Re: Mind Games
« Reply #20 on: Nov 4th, 2004, 12:43am » |
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If you consider the candles bits (1=burning, 0=extinguished),m then blowing at three candles is equivalent to XOR-ing them with 111
So basicly, you want to turn 1111111 to 0000000 by repeatedly XOR-ing it with 1110000, 0111000, 0011100, 0001110, 0000111, 1000011 and/or 1100001.
Clearly (if you know anything about XOR) it doesn't help to blow at the same three candles more than once.
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rmsgrey
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Re: Mind Games
« Reply #21 on: Nov 4th, 2004, 4:48am » |
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Yep, that looks like the right answers.
Having watched the repeat last night with a notepad beside me:
5) A sheet of plastic has a circular hole cut in the middle with diameter just larger than a 1p coin, so that 1p can be passed through the hole without distorting the sheet. The task is to pass a 2p coin through the same hole without distorting the coin.
For those who don't have UK currency handy, the 2p coin has a diameter roughly 25% more than that of the 1p coin, and both have the same height, which can be treated as negligible. The plastic sheet reallyoeshave negligible thickness, and can be bent freely, but can't be stretched - if you prefer, any line drawn on the surface will stay the same length whatever legal transformations you apply.
6) Not directly from the show, but a follow up to the birthday cake: While, as a 7-year-old, it's possible to find entertainment in extinguishing all 7 candles by blowing on each in turn, by age 16, the entertainment value is rather reduced, and the size of the cake is beginning to get rather alarming (fire safety rules dictate a minimum distance between conseutive candles) so the 16th birthday cake is square, and has candles set out in a 4*4 grid. The same rules apply - when you blow at one candle, you also affect its immediate neighbours, and whenever you affect a candle, you toggle its state between lit and unlit. For the grid layout, a candle's neighbours are the (up to) four joint-closest candles north, south, east and west (assuming the grid lines run north-south and east-west). What is the fastest way to extinguish all the candles on your 16th birthday? And how abou your 25th (a 5*5 square)?
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Grimbal
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Re: Mind Games
« Reply #22 on: Nov 4th, 2004, 8:57am » |
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6) ::
16 years:
_ X _ _
_ _ _ X
X _ _ _
_ _ X _ 4 puffs
25 years:
_ _ _ X X
X X _ X X
X X X _ _
_ X X X _
X _ X X _ 15 puffs (pffffff)
::
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Grimbal
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5)
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Grimbal
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Re: Mind Games
« Reply #24 on: Nov 4th, 2004, 9:30am » |
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on Nov 3rd, 2004, 8:56am, rmsgrey wrote:
Sorry Grimbal, but your solution isn't quite there - the amount of alcohol each isthe same, but it's divided differently... |
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Indeed, towr's solutions is much more elegant. It would even convince the people who drank the missing beer in all these glasses.
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