Hummings of a Happy Hurkle

See “the puzzle of the two switches” for a seriously hard logic puzzle. This is a variation of the same puzzle to make it even harder.

The puzzle is exactly the same, except that you can no longer assume anything about the initial state of the two switches. Each switch could be off or on.

Your challenge again is to devise a strategy whereby all prisoners can escape.

Solution over the fold.
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You are one of ten clever people about to be locked in a strange prison controlled by a computer. You will each be sent to individual isolated cells with no possibility of communication. Randomly, one cell door will open and the prisoner will be allowed access to a central room that contains two on-off switches, a keyboard and a screen showing the exit code. Each door has the same probability of opening. You can assume that both switches are off to start with.

A prisoner has two choices. If they enter the exit code on the keyboard they will be allowed out of prison, but the screen will then go blank. Doors will continue to open, but only those prisoners who can remember the exit code from a previous visit will be able to escape. If they flip either one of the switches they will then be allowed back to the cell they came from and the door will close again. Flipping more than one switch or any attempt to communicate with other prisoners will cause the computer to shut down, and lock all prisoners in forever.

Your challenge is to devise a strategy whereby all prisoners can escape. This means that all prisoners must have visited the room before the first one enters the exit code, and that they can communicate only by setting and observing the switches and the screen.

Solution over the fold.

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Andy and Bert have worked out a neat card trick, but they need your help to do it. The puzzle for you is to figure out how the trick works.

The essence of the trick is that you shuffle a normal pack of 52 cards thoroughlyand give 5 cards to Andy. Andy keeps one card, puts the others into a special order and gives them to Bert. Bert looks at the 4 cards and correctly names Andy’s card.

You can assume that the trick involves no deception and no communication to Bert other than the sequence of the 4 cards. Can you figure out how it is done?

Solution over the fold.
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This statement of the puzzle comes from Wikipedia. There are subtle variations, but only one puzzle.

Three gods A, B, and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are ‘da’ and ‘ja’ but you do not know which word means which.

You are free to ask any questions of any gods in any order to a total maximum of 3 questions. You may only ask questions that True and False can answer. For the purposes of this puzzle the Random god should be thought of as answering entirely at random with no regard for the content of the question. Differing interpretations of Random are responsible for some variations in the puzzle.

Solution over the fold.
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If you really have nothing better do then click the link. Don’t say I didn’t warn you.
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Tom just bought 100 animals for a total of $100. The 100 animals consists of sheep, pigs and hens.

The sheep cost $10 each. The pigs cost $2 each. The hens cost 50c.

How many of each animal did he buy?
It’s not too hard to solve by trial and error, but we are looking for a logical solution so we can be sure it’s unique.

Solution over the fold.

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If you don’t know what a boomershoot is, take a few seconds to speculate on what you might get if you put boomer and shoot together, in a US context.

http://boomershoot.org/

Be sure to check out the video. There is a link on how to make the stuff too.

The things some people get up to. I would too, except we seem to have laws against it.

Have you heard this one?
An infinite number of mathematicians walk into a bar.
The first one orders a beer.
The second one orders half a beer.
The third one orders a quarter of a beer.
The bartender interrupts the fourth: “How about I just give you 2 beers and let you all work the rest out.”

And another thing:
This atom walks into a bar. He says to the bartender, “I think I lost an electron here last night.” The bartender says, “Are you positive?”
Atom says: “No, I’m reduced.” Bartender says: “No charge.”

I guess not everyone will see the humour, but it sure tickles my funnybone.

Past, present and future walk into a bar. It was tense.

Midget clairvoyant escapes from prison. Headline: “Small Medium At Large!”

Puns are a rare medium well done.

Guy sends in ten puns to a magazine contest. Headline: guy fails to win prize, no pun in ten did.

Did you hear about the fire at the circus? It was intense.

A dyslexic guy walks into a bra.

Guy escapes from lunatic asylum and rapes a cleaner. Headline: “Nut screws washer and bolts.”

Red boat collides with blue boat. Both crews marooned.

A good pun is its own reword.

Ouch!

On Monday, you flip coins all day. You start flipping coins until you see the pattern Head, Tail, Head. Then you record the number of flips required, and start flipping again until you see that pattern, you record it, and start again. At the end of the day you average all of the numbers you’ve recorded.
On Tuesday you do the EXACT same thing except you flip until you see the pattern Head, Tail, Tail.

Will Monday’s number be higher than Tuesday’s, equal to Tuesday’s, or lower than Tuesday’s?

Solution over the fold.
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