010 - Prisoners and Switches

Twenty-three prisoners are imprisoned in an unusual prison. They are to be imprisoned until the warden of the prison decides to set them free.

The warden meets the prisoners as they arrive and tells them about a special room in the prison. In the room are two switches, each of which can be set either an "up" position or a "down" position. The switches are not connected to anything, and the warden does not tell the prisoners whether either switch is currently "up" or "down".

"I am about to give you an hour to plan, talking amongst yourselves," says the warden to the prisoners. "After that, you will be incarcerated in separate cells with absolutely no means of communication."

"From time to time during your imprisonment, I will select one of you at random and escort that prisoner to the switch room. The prisoner I select must select one, and only one, of the two switches and reverse its position. Then he will be led back to his cell. This is the only way in which the switches will be flipped; they will always be in the position that the last prisoner to visit the room left them in."

"The method by which I select a prisoner will be totally random and it may result in the same prisoner being selected several times in a row."

"At any time that a prisoner is in the switch room, he or she may announce to me, 'We have all visited the switch room.' If that prisoner is correct, you will all be set free. If they are incorrect, you will all be executed in a particularly painful manner."

What is the fastest way for the prisoners to win their freedom, without the slightest risk of being executed?

009 - Proving The Rule

In front of you are four cards. Each card has a letter or number printed on the face-up side. The cards read, in order:

A
Z
4
9

In the deck that these cards have been dealt from, all of the cards have a number on one side and a letter on the other.

If I told you that there was a rule, that cards which have an "A" on one side always have a "4" on the other, which two cards would you turn over to attempt to disprove the rule?

008 - Petals Around The Rose

In the game Petals Around The Rose, five regular six-sided dice are rolled, and players are challenged to give the "Petals Around The Rose" answer for the result.

For instance, the following dice rolls produce the following correct answers:

3, 5, 5, 5, 6 : the answer is fourteen
2, 6, 2, 1, 4 : the answer is zero
4, 3, 2, 1, 3 : the answer is four
6, 5, 6, 2, 2 : the answer is four
6, 3, 6, 5, 4 : the answer is six

There is only one correct answer for any given roll.

On a roll where the dice show 1, 3, 6, 5, 6, what is the "Petals Around The Rose" answer?

007 - Poison Pills

While captured by the evil Dr Apocalypse, you are presented with a terrifying deathtrap.  In front of you are five seemingly identical bottles full of pills, and a set of scales.

"Four of these bottles," explains Dr Apocalypse, "contain harmless sugar pills.  Each of the harmless pills weighs 10 grams.  One bottle, however, contains deadly poison that will deliver you to a painful death. Each of the poison pills weighs 9 grams."

"You may open the bottles, look at the pills, and use the scales I have provided you with once and once only.  After you have made a single weighing of your choice, you must correctly identify the bottle of poison, or else be forced to eat a pill from it."

The scales are of the sort that return the total weight of everything placed on them (that is, pressure scales, not balancing scales).  All the pills are shaped identically, and you're not allowed to weigh a pill and then keep adding more while still checking the weight. Only one weighing of as few or as many pills as you want, at once, is allowed.

How can you be certain which is the poison bottle?  And what is the smallest number of pills you can weigh to arrive at that conclusion?

006 - Two Sons

In the town of Gentford, newborns are equally likely to be male as female.  Out of all inhabitants of Gentford who have at least one son, Gunther is typical.  He has exactly two children.  What is the probability that he has two sons?

(For the purposes of this puzzle, assume that gender options in newborns are limited to "male" or "female".)

005 - Five Daughters

Mary's father has five daughters: 1. Nana, 2. Nene, 3. Nini, and 4. Nono.  What is the name of the fifth daughter?

004 - Pigs In A Poke

Farmer Joe's Pig Farm lies on the border of Oddsville and Four Hills, and is thus subject to the laws of both towns.  Four Hills requires all pig farms to have exactly four pig pens, no more, no less.  Oddsville requires that all pig pens hold an odd number of pigs greater than zero.

Farmer Joe has 21 pigs.  How can he comply with both laws without moving his farm, changing his business, or gaining or losing pigs?

003 - The Bridge and the Torch

Four people come to a river in the night. There is a narrow bridge, but it can only hold two people at a time. Because it is night, a torch has to be used when crossing the bridge. Person A can cross the bridge in 1 minute, B in 2 minutes, C in 5 minutes, and D in 8 minutes. When two people cross the bridge together, they must move at the slower person's pace.  The group only has one torch between them.  How can all four people get to the far side of the bridge in 15 minutes or less?

002 - Isolate

Add additional walls to the pictured grid so that:

* It is broken into seven (7) discrete areas, of the following number of squares: 2, 3, 3, 3, 3, 4, 7.

* Each area contains exactly two gray cubes; no more, no less.

* Each grid intersection (marked by a plus sign) connects to at least 2 walls.

Lines may only be vertical or horizontal.

001 - The Mutilated Chessboard

Suppose a standard 8 x 8 chessboard has two diagonally opposite corners removed, leaving 62 squares.

* Is it possible to place 31 dominoes of size 2 x 1 so as to cover all of these squares?

* Explain why without showing a picture of a chessboard.

About Serendipity Puzzles

Serendipity Puzzles is a private puzzling competition created by me, for friends.

Puzzles are made available each weekday by email. Each puzzle appears on this blog at 8 PM Australian Eastern Coast Time the day before it is due to go out by email. Answers are submitted by email to me. Correct answers score points on a leaderboard that is distributed roughly twice a week by email.

At this stage new players are welcome. To join, please email me at starfall2317, at gmail.

I reserve the right to not accept new players, to post puzzles at times of my choosing, to discontinue the puzzling competition at any time, and to accept or refuse answers entirely at my discretion.

Comments are disabled on this blog to prevent spoilers.