I look after a bunch of recalcitrant high school kids for a few hours each week. They are generally an affable crew and often I will finish with a logic puzzle to finish a session, which if answered correctly allows them to leave early.

If they thought of it as having to use their brain on top of school work they probably wouldn't have a bar of it but they approach it almost as a form of sport.

Often I will have groups staying well past the time they could go trying to work through to the answer.

The lure of a good logic puzzle seems to be fairly universal.

However since many of the kids are repeat offenders and they are across my kit bag.

My hope is for a contribution or two. Answers from the poster are not required since if the rest of us can't work them out some of my lot might struggle, but I would prefer less of the hanged man with a pool of water at his feet or the dwarf in the lift and more of the logically consistent type.

That being said simple answers to complex questions are always welcome. For instance;

How many grooves are there on a 45rpm record that plays for 30 minutes a side, has an external diameter of 35cm and an internal diameter (where there are no grooves for those who are not familiar with LP records) of 5cm ?

Here is an appetizer;

Three crates of fruit wash up on a desert island which you are marooned on. One is labelled Oranges, another Apples and the third Apples and Oranges. As soon as you lay a finger on the first a Genie appears and says, “Not so fast, before you can eat any fruit you must choose one crate to reach into and without looking remove one piece of fruit. From it you must identify the fruit in all three crates since they are all currently marked incorrectly. You only get one chance.”

What do you do?

Awaiting your favourites if you have any. Thanks.

Do you mean things such as, "How much soil is there is a hole in the ground 2.3m long by 1.7 m wide and 3.2m deep?"

or "A rope ladder with 25 rungs hangs over the side of a ship. Its rungs are 30cms apart with the bottom one just touching the water. The tide is rising at 18cms an hour. How long until 3 rungs are covered by water?"

or are they too simple? But my favorite is:

>>WORLD'S EASIEST QUIZ
(Passing requires 4 correct answers)
Please answer all questions before scrolling down for the answers.

1) How long did the Hundred Years' War last?
2) Which country makes Panama hats?
3) From which animal do we get catgut?
4) In which month do Russians celebrate the October Revolution?
5) What is a camel's hair brush made of?
6) The Canary Islands in the Pacific are named after what animal?
7) What was King George VI's first name?
8) What color is a purple finch?
9) Where are Chinese Gooseberries from?
10)What is the color of the black box in a commercial airplane?

All done?
Remember, you need 4 correct answers to pass.<<

Answers available if required

This is somewhat lame (along the lines of the
hanged man and the pool of water) but here goes anyway.
I'll try to come up with something better next time:

A man is found dead on a little island.
He was alone on the island.
He did not starve or commit suicide.
He wasn't poisoned or killed by a wild animal.
How did he die?

Answer available on request - but I'm sure
you'll work it out. ;-)

Re, apples and oranges, since ALL the boxes are marked incorrectly, you should reach into the "mixed" crate.

If you pick an apple, then the "orange" crate is mixed and the "apple" crate contains oranges.

If you pick an orange, then the "apple" crate is mixed and the "orange" create contains apples.

Lexi, I believe that the man drowned and his body was carried to that island.

The lost dollar?

Three businessmen sit down for lunch in a restaurant advertizing a $10 special, which they all order.

The bill for $30 arrives but they complain and tell the waiter that the meal was not that good and wanted a rebate.

The waiter returns to the cash desk with the $30 and tells the owner about the complaint.

The owner takes five one dollar coins from the till and says OK; give them this discount as a sign of good faith.

The waiter can’t work out how to split $5 between three customers so he sticks $2 in his own pocket.

Back at the table he apologizes and gives each customer $1 back.

So each customer has now handed over $10 and got a $1 rebate. So each paid $9?

3 x $9 = $27, Plus the $2 the waiter pocketed = $29?

Where has the other $1 gone?

"Where has the other $1 gone?"

You should not add the $2, but subtract it:

The owner received: 3 X $9 - $2 = $25

Thanks for the contributions thus far.

Dear WmTrevor,

The hole in the ground reminds me of the plane that crashed into the cemetery directly on the border between North and South Dakota, one thirdof the passengers were Catholic and two thirds were Protestant, where were the survivors buried?

The tide one I used a few weeks ago. Always gets them for bit. Good puzzle that.

I managed six.

2-Ecuador, 3-sheep, 4-November, 6-canines, 9-New Zealand (lived there), 10-orange I think.

Dear Lexi,

I am certainly not adverse to these types of puzzles, I enjoy having them posted here and trying to nut them out. The reason for my original remark was purely practical, the hanging man over a pool of water required me to answer about 50 queries from the kids. When you have two or three groups going at once it can be a bit hard to handle.

Was Yuyutsu's answer the one you had in mind? Or was it old age?

Dear spindoc,

This has to be one of my favourites and used it again last session. Oh what fun, especially the looks on their faces when you first deliver it. It is probably cruel when you know they almost have it and you say "you just aren't getting it" then restate the question, it throws them all off completely.

Another favourite is the two jars of exactly the same quantity of nutrient fluid. Into the first we put one amoeba which divides once every 3 minutes. It takes 1 hour and 57 minutes to completely fill the jar. In the second we place two amoebas, how long does it take to fill it completely?

Those amoeba - one minute 54 seconds.

Beautifully counter-intuitive...

csteele, try this one then.

James lives in Sydney, he has two girlfriends, he likes both equally.

So when he goes on dates, he goes to the train station and lets the train decide which he visits, the first train to arrive is the one he visits. One girlfriend lives on the northern line, the other on the southern line, both equal distances from his train station. Each train arrives at 10 min intervals precisely.

He finds himself visiting the girl in the north eight times out of ten, why?

The government of Tulpania declared Mt. Kunusuma as a nature reserve, totally out of bounds: nobody ever scaled it and a whole regiment guarded its perimeter day and night against trespassers.

However, Tulpania ran into a bad deficit and when Bill Gates offered them $2b for allowing him to be the first person to climb Mt. Kunusuma, they could no longer refuse.

He started off climbing in the morning and by the evening when he reached the peak, he found there a cabin. He opened its door and found 3 decaying human bodies inside.

The Prime-Minister of Tulpania insisted that he was the first ever to climb Kunusuma - and he did not lie. How come?

Spindoc, the South-bound train always arrived 2 minutes after the North-bound train.

Dear spindoc,

I think the answer is that although the frequency of each individual train is ten minutes the South bound train arrives two minutes after the North bound one leaves the station so unless he arrives within that two minutes out of every ten he will be headed north.  Not bad. Into the kit bag. Thanks.

Dear Pericles,

Indeed it is. One I reserve for the slightly more mathematical students is how many people must enter a room before the chances of two of them having a birthday on the same day of the year is better than 50%?

It has won me more than a few drinks in bars.

Dear Yuyutsu,

Beat me to the punch.

As to your puzzle a ballooning accident or arrival by helicopter would deliver three bodies without necessitating climbing but the cabin has thrown me for now. Leave it with me.

Hi csteele, This time with answers (for a cut and paste):

1) How long did the Hundred Years War last? 116 years
2) Which country makes Panama hats? Ecuador
3) From which animal do we get cat gut? Sheep and Horses
4) In which month do Russians celebrate the October Revolution? November
5) What is a camel's hair brush made of? Squirrel fur
6) The Canary Islands in the Pacific are named after what animal? Dogs
7) What was King George VI's first name? Albert
8) What color is a purple finch? Crimson
9) Where are Chinese gooseberries from? New Zealand
10) What is the color of the black box i n a commercial airplane? Orange, of course.

Check out this for an excellent selection pf puzzlers:
http://pdfbooks.co.za/unpublished_work/Van_Der_Westhuizen_CH/mindbenders.pdf

(Arjay would point out Pericles that that can't be right because it doesn't allow for the BMIC stealing the amoebas' productivity)

It's the cabin of a crashed plane.

And 23 people.

Gotta love this stuff!

Here's the answer to my earlier puzzle:

He was on a traffic island and was hit by a car.

This is fun!

You may have used this with your students already. This puzzle made an appearance during a mathematics lecture in a scene from the film '21' and also featured in the book 'The Curious Incident of the Dog in the Night-Time' by Mark Haddon.

This puzzle deals with probabilities.

On a Game Show set there are three closed doors. Behind one of these doors is a car and behind the other two are goats.

The game begins by the contestant picking a door but the door is left shut for the moment. The Host then opens one of the remaining doors which he knows will reveal a goat.

After the Host opens the door to reveal a goat, the contestant is given the option to switch doors or stay with their first choice.

What is the probability of winning the car if the contestant stays with the first choice and what is the probability if the contestant switches doors? Are the chances improved by switching doors, staying or are they the same?

Please put me out of my misery… No matter how I calculate it those amoebas are going to take one hour and 54 minutes. What am I missing?

Dear Pericles,

Of course, I hang my head in shame.

And 23 is correct.

Here is one that throws a few initially.

A four sided stone plinth about a metre high and around 10cm width was discovered in some Roman ruins. At the top was a metal ring of again 10cm diameter. Down one side were inscribed with what look like five Latin words chiseled down the face ;

TOT
IEH
ORS
E
STO

What was it used for?

Dear pelican,

Yes I know it as the Monty Hall problem. It is a beauty. I have an 'uncle' who is a book maker, lives his life with odds yet to this day can't get his head around it. Still thinks I am stooging him. The back story is great too. 

http://en.m.wikipedia.org/wiki/Monty_Hall_problem

Why over 1000 Phd holders wouldn't pause before writing in to tell a woman with an IQ of close to 200 she was wrong is baffling. Arrogance I suppose. Even the esteemed Paul Eros got caught as did the US Director General of Mathematics.

Dear WmTrevor,

Lol. You are of course correct. Pericles moved the decimal point so to speak.

Big sigh of relief… After 20 minutes of maths that's what I hoped, but your "Dear Pericles, Indeed it is." led to a terminal case of self doubt and the return to Economic Statistics textbooks that hadn't been opened for years.

Pericles you are temporarily sin-binned as the "Serafim of posters of clarity on OLO" to Cherubim status. (Looks like Arjay was right! or is it left)

Should that plinth not have read "Ligare equos ad"

I found this one on the web:

It is purported that Einstein said 98 percent of the
world's population could not figure out this logic
problem. Let us know how long it took you:

There are 5 houses each with a different colour.
Their owners, each with a unique heritage,
drinks a certain type of beverage, smokes a
certain brand of cigarette, and keeps a certain
variety of pet.

None of the owners have the same variety of pet, or smokes
the same brand of cogarette, or drinks the same beverage.

CLUES:

The Brit lives in the red house.
The Swede keeps dogs as pets.
The Dane drinks tea.
Looking from in front, the green house
is just to the left of the white house.
The Green house's owner drinks coffee.
The person who smokes Pall Malls raises birds.
The owner of the yellow house smokes Dunhill.
The man living in the center house drinks milk.
The Norwegian lives in the leftmost house.
The man who smokes Blends lives next to the one
who keeps cats.
The man who keeps a horse lives next to the man who smokes
Dunhill.
The owner who smokes Bluemasters also drinks beer.
The German smokes Prince.
The Norwegian lives next to the blue house.
The man who smokes Blends has a neighbour who drinks water.

Who owns the pet fish?

Answers will be provided on request.

Achtung, ve vill ask de questions ... nein?

Great thread but Lexi, not sure yours above would challenge a bunch of recalcitrant high school kids :)

Oh, the shame of it...

>>Pericles moved the decimal point so to speak<<

Just deserts, WmTrevor...

>>Pericles you are temporarily sin-binned as the "Serafim of posters of clarity on OLO" to Cherubim status<<

Not sure even that will cut it. I'll accept demotion to Belial for the time being, and work my way back.

Redemption available - A Harder Fork...

In the Road. (A bit of an oldie - but a goodie)

Upon your death you find yourself walking along a road in search of heaven. You come to a fork in the road and instinctively know that one road leads to heaven and the other leads to hell, but you do not know which is which.

At the fork are a devout truth teller (resident of heaven), a devout liar (resident of hell), and a resident of limbo who randomly tells the truth (sometimes he lies, sometimes he tells the truth, but with no regularity for either).

Although you know these characteristics of the individuals, you do not know who is which. You are allow two questions (non-compound type without 'and', 'or', 'but', etc.) and may direct these two questions to any individual (either both questions to one individual or one question to one individual and the other question to a different individual).

What two questions would you ask so that you would positively find heaven? NOTE: A question cannot be asked which will cause the respondent to reply 'I do not know'.

Wasn't this in the movie Labyrinth?

This 'resident of limbo who randomly tells the truth' seems a new twist to me and I think it's redundant.

You only need ask 1 question too.

Ask one of the people "what would the other one say is heaven?" then take the opposite.

If it was the liar you asked, he would point to hell, because the honest one would say heaven.
If it was the honest one, he would point to hell too because the liar would point to hell.

Hi csteele

For me, I like "thought experiments" or ways of explaining quite complex ideas in ways that 'bring it home' - even for the recalcitrant.

While not quite in the same league as some of the riddles already presented, I'm sure even high-schoolers can get a buzz out of these, particularly if they can stir moral reasoning - assuming they have them of course.

See these:

http://www.toptenz.net/top-10-most-famous-thought-experiments.php

Have to say one of my favourites is Einstein's light beam - but, it's all relative :)

.

Confession:
Lexi, it only took me 5 seconds - I struggled with that one years ago when then, maybe an hour or so ! Chaos in motion, with spaghetti diagrams and charts strewn accross the floor !!

Dear Bonmot,

My next door neighbour is still working on it.
I gave it to him this afternoon.
Anyway for those of you who want to know the solution
here it is:

http://www.brain-fun.com/Brain-Teasers/EinsteinsRiddleAns.php

Dear Lexi,

I had done your puzzle years before but thought to get a time. Couldn't nail the sucker, tried three times. Finally back tracked and I had written down the Green house owner as drinking Tea! It is a good puzzle and I have given a similar one to the kids usually allowing the whole group to work on it together. I generally keep it for rainy days.

There are 5 ships in a port:

1. The Greek ship leaves at six and carries coffee.
2. The Ship in the middle has a black chimney.
3. The English ship leaves at nine.
4. The French ship with blue chimney is to the left of a ship that carries coffee.
5. To the right of the ship carrying cocoa is a ship going to Marseille.
6. The Brazilian ship is heading for Manila.
7. Next to the ship carrying rice is a ship with a green chimney.
8. A ship going to Genoa leaves at five.
9. The Spanish ship leaves at seven and is to the right of the ship going to Marseille.
10. The ship with a red chimney goes to Hamburg.
11. Next to the ship leaving at seven is a ship with a white chimney.
12. The ship on the border carries corn.
13. The ship with a black chimney leaves at eight.
14. The ship carrying corn is anchored next to the ship carrying rice.
15. The ship to Hamburg leaves at six.

Which ship goes to Port Said? Which ship carries tea?

My time on that is 23 minutes.

Thanks for the link bonmot. My phone refuses to open it so will check it out once I'm in front of a computer.

Dear Houllebecq,

The liar and the truth teller is one I have given numerous times but WmTrevor's example extends it nicely. 

Dear WmTrevor,
Why am I getting 'Subnecto ferrum ut?'. In any case you are correct.

Dear csteele,

Thank You for the 5 ships puzzle. I also must confess
that I've done it previously. My son used to love the
Einstein puzzles - so we've covered quite a few.

I'll try to find something different for you.

Dear WmTrevor,

I have been through the "If I asked your two friends 'is the left road the way to heaven?', would my chances be better than asking you?" to no avail.

I think I'm close.

I feel sure there is a hole in it some where, though I'm not sure where exactly, but it seems to work.

Might not you ask any of them the following?

"If I asked 'Is the path to the left the way to heaven?' would you answer me 'Yes'?"

If the answer is 'Yes' take it, if 'No' take the one to the right.

Best I can do for the minute. My brain is about to explode.

Dear Lexi,

Both are great. The best part is even with a big bunch they all get a chance to have some input on problems like this.

This has been a bit of a winner recently;

You have a dozen bags of gold. However one of them has been substituted with counterfeit coins. The only difference to the real ones is they weigh a gram lighter than the others.

You need to find our which bag contains the counterfeit coins but you only have a single set of scales on which you are allowed only one weighing.

How do you tell which bag it is?

"Add iron to?" Don't know, csteele… Are you trying to put your nickname through Google translate? Which for my Latin was all I did with 'to tie horses to'. To the oldie but goodie, you don't need to do any better.

(Houllebecq I was too busy trying to work out the plot of Labyrinth to notice any puzzles - but for the most difficult iteration check out "the hardest logic puzzle" at Wikipedia.)

I went looking for something that was very difficult, practical, could be 'performed' to demonstrate it had been solved/learned and had a touch of 'mind reading' about it. It also allows a small group work and requires planning and partner cooperation to 'work'.

Your students might enjoy this because they can practise it with cards themselves after the solution is provided. I've included the solution because even with the answer the puzzle is still impenetrable.

>>The Card Trick

I ask Alex to pick any 5 cards out of a deck with no Jokers.

He can inspect then shuffle the deck before picking any five cards. He picks out 5 cards then hands them to me (Peter can't see any of this). I look at the cards and I pick 1 card out and give it back to Alex. I then arrange the other four cards in a special way, and give those 4 cards all face down, and in a neat pile, to Peter.

Peter looks at the 4 cards i gave him, and says out loud which card Alex is holding (suit and number). How?

The solution uses pure logic, not sleight of hand. All Peter needs to know is the order of the cards and what is on their face, nothing more."

So there's no mental trauma...

Here is the hint and the answer:
>> There are only 4 suits, so there will be at least two cards of one suit, one higher and another lower. By careful selection and placement the cards can be used to encode the exact number and suit of the selected card.

Answer: Pick out two cards of the same suit. Select a card for Alex where adding a number no greater than six will result in the number of the other card of the same suit. Adding one to the Ace would cycle to the beginning again and result in a Two. E.g. if you have a King and a Six of Diamonds, hand the King to Alex. The other three cards will be used to encode a number from 1 through 6. Devise a system with Peter to rank all cards uniquely from 1 to 52 (e.g. the two of hearts is 1, the two of diamonds is fourteen etc...). That will allow you to choose from six combinations, depending on where you put the lowest and highest cards.<<

The source link: http://www.folj.com/puzzles/very-difficult-analytical-puzzles.htm?5#card

I perceive the logic but I'm going to keep at this until I think I comprehend the answer – but my brain hurts.

Dear WmTrevor,

I'm still a little uneasy about the Limbo guy flipping halfway through but if you are happy I'll take it.

The five card trick is one I used to do with my daughter when she was quite young. Always bedazzles the crowd and for some reason she used to get all the kudos and loved it even though I did all the arranging. Now she is a teenager it is too embarrassing. Will have to wait for grand kids I suppose.

However I never once stopped to think why it worked.

As to the Latin I am going to have to stay away from  cheap translators, Google does indeed return your line. I think I might have been trying to shoe mine.

My favourite puzzle of all time requires no gimmicks just concentration and patience.

It took me over half an hour and is probably the most satisfied I can remember ever being after completing a puzzle.

I will have to rely on a description due to the limitations of the medium but here is my best.

A piece of carpet is 9' x 12' and is solid except for an 8' x 1' hole cut directly in the middle running length ways. The task is to cut it into two pieces only so when it is rejoined it forms a 10' x 10' square solid piece.

Great one for a rainy day.

Thanks all for the contributions thus far. Some have definitely made it into the kit bag.

Dear csteele,

Thanks for this thread.

It's been fun and can be moorish so I'd better
quit while I'm still able to function.
BTW - I know this is a bit off topic -
we went to see the movie - "Margin Call,"
tonight -
starring Kevin Spacey, Jeremy Irons ...
It was advertised as "better than "Wall Street,"
and it did not disappoint.
Excellent cast - and absolutely
riveting. Highly recommend it. If you
haven't already seen it.

How about simple bloody-mindedness like the shredder challenge?

Please excuse embedded retro gamer reference.

Rusty

This one's an oldie, but it's pretty neat and tidy.

An anthropologist is studying a couple of tribes in a jungle in South America. One of these tribes always speaks the truth. These people are helpful and honest. The other tribe is a group of cannibals who always lie.

One day, the anthropologist is being pursued by some of these cannibals. He comes to a fork in the road. He knows from his maps that one way leads to the home of the good tribe, who will help him. One path leads to the evil tribe, who will eat him alive.

Unfortunately, he doesn't have his map with him and he can't remember which way to go.

There is a tribesman standing at the fork. The anthropologist only has time to ask one question - what single question will tell him the correct path?

Dear Rusty,

The shredder challenge look interesting. If it were run today I wonder how many would choose to simply outsource the sucker to India?

Dear TurnRightThenLeft,

The question is of course “If I ask your mate what is the way to the village which way will he point?” you then take the opposite route.

I have used this several times to good effect.

No one has answered the question of how many grooves in a 45RPM record yet. Care to take a stab?

Dear csteele,

How many grooves on a 45rpm?

One (spiraling) on each side.

In other words - two.

Nice try csteele - there's no mate. Just one guy.

Dear Turnrightthenleft,

Ah ha. Yes. Sorry my misreading.

The best I can do is the same as the answer I gave to WMtrevor's problem;

You would to put to the man the following;

If I asked 'Is the path to the left the way to the village?' would you answer me 'Yes'?"

If the answer is 'Yes' take it, if 'No' take the one to the right.

A good puzzle. Thank you.

Dear Lexi,

Well done, that is unless the record was by Marvin Gaye then there would be 10 + 1 each side.

csteele, a hint re TRTL... "If I asked someone from the other village... what would they say?"

And... this isn't a puzzle as such but you could turn it into a competition question for the students. It's a 'factoid' that still makes my brain ache at the unimaginable scale of it...

If the coldest temperature is absolute zero. What's the hottest temperature?

(From the BBC's Dr Chris Smith and the naked scientists – 26 March 2012.)

Answered by Sam Gregson, high energy particle physicist at the University of Cambridge and working at the Large Hadron Collider in Cern, Switzerland.

"The temperature of a system is simply related to the amount of energy in a system. Because a system can't have a negative energy there is only so much heat you can remove from it and so a limit to how cold you can actually get. This is called absolute zero. We have got very close to it.

Scientists in Finland have cooled rhodium atoms to a 10th of a billionth of a degree above absolute zero.

On the other hand an absolute maximum temperature would require there to be a limit to the amount of energy you could give to a particle and as far as we know there is no such limit.

Although the speed of light is the universal speed limit the reason you can't get there is that this would require an infinite amount of energy. So this speed limit does not limit the amount of energy and therefore the temperature of an individual particle.

The most energetic particle ever observed was a cosmic ray over Utah travelling at 99.99999999985% of the speed of light, probably a single proton, with about 50 J of energy.

This is equivalent to about 5,000,000,000,000,000,000,000,000 (trillion trillion) degrees Celsius. And there is no evidence that this is the hottest you could get to.