Mastermind

Some puzzles are derived from games, such as chess problems, draughts problems or bridge problems. It is rare that a game is built around a puzzle. One such a game is Mastermind, invented by by Mordecai Meirowitz, an Israeli postmaster and telecommunications expert.

For those who don’t know it (are there any such persons in the ‘civilised’ world?), here are the rules. The board is four columns white, and one player sets up a secret combination of colours by selecting 4 pegs from a set of pegs in six colours, as shown in the picture.
The second player has to guess this combination. He may put up his own combination, and the first player will respons with one black peg for every peg with a colour in the correct spot and a white peg for every peg with the colour in the wrong spot. Pegs with a colour which are not in the secret combination are not rewarded at all.

1) 4 colours on 3 spots^*

2) 6 colours on 4 spots^**

There are several variations of the game.
The standard form is one codemaker and one codebreaker. Roles alternate to see who can solve the others pattern is as few guesses as possible. Or in the shortest time.
An alternative is to have several code breakers, not able to see each others guesses, and competing for the fewest number of guesses.
Instead of using colours, one may use digits (0-9), or letters. In the latter case, players are limited to existing words.
More Mastermind puzzles are planned in one of the upcoming e-books.

You can check your solution here for no 1 and here for no 2

A new puzzle is published every friday, at which time I will also post the solutions to the previous weeks puzzle so you can check yours. I welcome your solution times, but please don’t publish your solutions – that might spoil the fun for others. I also welcome your remarks on the difficulty level, multiple solutions, ambiguities and so on.

Riddles

Some puzzles are more like riddles. Here are some classics:

1) Ox
A farmer in Asia is ploughing his land with a cow. His field is 123 feet long.
With each of its four legs, the cow makes 2 footprints for every feet it walk.
When the farmer walks back along the last straight furrow, how many footprints will he count?

(This one is based on an old problem going back to the middle ages, see the Propositiones by Alcuin of York)

2) Railway crossing
What are the colours on the boom barrier of an uncontrolled railway crossing in Australia?

3) Legal trouble
A plane belonging to a British company with German passengers, crashes on the border between the USA and Canada. In which country will the survivors be buried?

4) More legal stuff
In Belgium, is it legal for a man to merry his widows sister?

Sums with swapped doubles

In this type of puzzle: swap two pairs of digits to make the addition correct. For example, in the illustration above the 7 and the adjacent 0 might have been swapped, or the 3 with one of the 8’s. Your task of course is to restore the original correct sum by finding the two swaps.

1) nr 1^*

1486
3172
—-+
7313

2) nr 2^*
3155
4349
—-+
7317

3) nr 3^*
2748
6146
—-+
6134

4) nr 4^*
9559
1326
—-+
5418

5) nr 5^*
See the illustration at the top of this post.

Nr 3 comes from Issue no 41, 1975, of the famous British magazin Games and Puzzles. I suppose an anonymous editor came up with this puzzle type.
If you have other information about the origin of this puzzle type, I’d love to hear it.

You can find the solutions at 137, 147, 157, 167 and 177

,

Camel inheritance

1) How many camels?*
The sheik has died. When the Mullah read the will, he found that the sheik had left each of his five sons 1/6 of his camel herd, while his only daughter in an act of sheer discrimination inherited only 1/8th of the herd.
The mullah solved it for the kids without butchering a camel.
How many camels did the sheik have?

You can check your solution.

The puzzle above is a new one, and of course derived from the following classic:
2) 17 camels and three sons**
The sheik has passed away. When the mullah opens his will, he finds the sheik has left 1/2 of his camels to his oldest son, Achmed, 1/3 to the second son, Harim, and 1/9th to poor Bahari, the youngest. Now one of the sheiks camels had died in an accident a month ago, leaving only 17 camels to be divided.
How did the mullah divide the camels without butchering one?

This puzzle is based on a problem which according to some was first posed by Gaston Boucheny, “Curiosités et Récréations Mathématiques”. Paris, 1939. The French ed. of MRE says it is a problem of Arabic origin, while Kraitchik, Math. des Jeux, says it is a Hindu problem. The claim attributing the puzzle to 1939 seems wrong to me, as Sam Loyd and Henry Dudeney posed the problem in the Strand magazine years earlier. In fact, this puzzle was included in Henry’s puzzle book: “536 Puzzles and Curious problems” as number 172.

There is a hint.

3) The seventeen horses**
“I suppose you all know this old puzzle” said Jeffries. “A farmer left his seventeen horses to be divided among his three sons in the following proportions: one half to the eldest, one third to the second, and one ninth to the youngest. How should they be divided?”
“Yes, we all know that”, said Robinson. “But it’s impossible. The answer given is always a fallacy.”
“I suppose you mean,” Progers suggested, “the answer where one horse is borrowed, so that the division can be done without butchering a horse, the sons receive9, 6 and 2 and the extra horse is returned”.
“Exactly!” Robinson replied “And each son receives more than his share.”
“Stop!” cried Benson. “If each man receives more than his share, the total must exceed 17 horses, but 9, 6 and 2 neatly sum up to 17.”
“That indeed looks queer”, Robinson admitted, “but 17/2 is 8,5, not 9. so the oldest son receives more than his share. And it’s similar for the other sons. The thing can’t really been done”
“And that’s where you all are wrong”. Jeffries stated. “The terms of the will can exactly be carried out, without any mutilation of a horse.”
To their astonishment, he showed them how it was possible.

There is a hint.

Oh, the image at the top of this page is the coat of arms of Zurich, available under GFDL license and created by Ronald zh.