Category Archives: Uncategorized

Eleusis


There are few good puzzle games. Puzzles rarely make good games, and good games rarely contain puzzles.

The first classical exception is mastermind. In recent years, Escape room shave become popular. A game which I learned as a student is Eleusis. This post concentrates on Eleusis. I wrote about Eleusis before in December 2013, you can find that post here.

The game of Eleusis was invented by Robert Abbott in 1956, and is totally different from such games as bridge or poker. Eleusis is played with a standard card deck of 52 cards. One player thinks of a secret rule and preferably writes this down. He plays two cards which obey the secret rule. All other players receive a number of cards, for example each player receives 5 cards.

The two cards are the beginning of a line of cards. The other players now take turns in playing a card to the end of the line. When a player plays a card, the Rule Inventor indicates whether the card obeys the rule. If it does, it is added to the end of the line. If it does not, the card is placed below the line and the player draws two extra cards from the deck. In both cases, the turn passes to the next player. The player who first gets rid of all his cards wins.

In the image above, the Rule Inventor started the row with 10 of clubs and jack of spades. The first player played 3 of spades, which was wrong. The next two cards, 3 of diamonds and 6 of spades, were also wrong. The fourth player tried 9 of hearts, which was correct.

The question is of course: With your hand depicted at the bottom, which of the 5 cards labeled A-E do you play?

You can check your solution here

The same coffee


The same coffee*/*****
My wife and I visited a restaurant. When my wife found a fly in the coffee, I called the waiter, who took the cup away and returned with a fresh cup.
As the waiter walked away, my wife angrily called him back and said: “You brought me the same coffee!”

How did she know?

You can check both your solutions here

New puzzles are published at least twice a month on Friday. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars.

Cryptarithm – authors


Replace every letter by a digit to get a correct addition.

authors****/*****
cryptarithm-2016-12-01-authors-exercise

You can check your solution here

New puzzles are published at least twice a month on Friday. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars.

From 5 to 4


Consider the following figure:
matches 5 to 4 squares exercise

It is made of 12 matches, it is 1 figure, its circumference is 12 matches long and its surface is 5 squares. Can you reaarange them in such a way that it is still made of 12 matches, thats its circumference is 12 matches long, 1 figure but its surface is just 4 squares large?

You can check your solution here

Christmas puzzles


For Christians, Christmas means that God is not just a distant being who judges us miserable beings from far away up in heaven, but is someone who became like us: he was born as a baby in Bethlehem.

For most people in the western world, it means having one or more days off, meeting family, and having fun. Fur puzzlers, mean having time so solve a few brainteasers. For this occasion I dug up some classic christmas teasers.

In “The Canterbury puzzles” H.E. Dudeney tells of the squire’s Christmas puzzle party. One of them was:
1) Under the mistletoe bough
canterbutry puzzles 092
“At the party was a widower who has but lately come into these parts” says the record; and to be sure, he was an exceedingly melancholy man, for he did sit away from the company during the most part of the evening. We afterwards heard that he had been keeping a secret account of all the kisses that were given and received under the mistletoe bough. Truly, I would not have suffered anyone to kiss me in that manner had I known that so unfair a watch was being kept. Other girls were in a like way shocked, as Betty Marchant has since told me.” But it seems the melancholy widower was merely collecting material for the following little osculatory problem.

The company consisted of the squire and his wife and six other married couples, one widower and three widows, twelve bachelors and boys, and ten maidens and little girls. Now everybody was found to have kissed everybody else, with the following exceptions and additions:
No male, of course, kissed a male. No married man kissed a married woman, except his own wife. All the bachelors and boys kissed all the maidens and girls twice. The widower did not kiss anybody, and the widows did not kiss each other. The puzzle was to ascertain just how many kisses had been thus given under the misstletoe bough, assuming, as it is charitable to do, that every kiss was returned – the double act being counted as one kiss.

You can check your solution at here

2) The Christmas Geese
Squire Hembrow, from Weston Zoyland—wherever that may be—proposed the following little arithmetical puzzle, from which it is probable that several somewhat similar modern ones have been derived: Farmer Rouse sent his man to market with a flock of geese, telling him that he might sell all or any of them, as he considered best, for he was sure the man knew how to make a good bargain. This is the report that Jabez made, though I have taken it out of the old Somerset dialect, which might puzzle some readers in a way not desired.
“Well, first of all I sold Mr. Jasper Tyler half of the flock and half a goose over; then I sold Farmer Avent a third of what remained and a third of a goose over; then I sold Widow Foster a quarter of what remained and three-quarters of a goose over; and as I was coming home, whom should I meet but Ned Collier: so we had a mug of cider together at the Barley Mow, where I sold him exactly a fifth of what I had left, and gave him a fifth of a goose over for the missus. These nineteen that I have brought back I couldn’t get rid of at any price.”
Now, how many geese did Farmer Rouse send to market? My humane readers may be relieved to know that no goose was divided or put to any inconvenience whatever by the sales.

You can check your solution at here

Sam Loyd, of course, also had a nice christmas puzzle, though it disappoints me a bit that a quick scan revealed just one:
3) The Christmas Turkey
Loyd 136 the christmas turkey
Here is a pretty puzzle for the juveniles which affords considerable scope for ingenuity and cleverness. This Turkey Gobbler has led “Jolly old Santa Claus” a merry chase around the field, as shown by the tracks in the snow, before he was caught. You can see that they entered from the right side and did some lively circling before arriving at their present position, where the gobbler seems to be upon the point of surrendering. Our young folks are asked to study the situation carefully and to tell just how many times Santa Claus must have turned completely around during the chase, before pouncing upon the turkey?

You can check your solution at here

Please try to solve the puzzles on your own. You are welcome to remark on the puzzles, and I love it when you comment variations, state wether they are too easy or too difficult, or simply your solution times. Please do not state the soultions – it spoils the fun for others. I usually make the solution available after one or two weeks through a link, which allows readers to check the solution without the temptation to scroll down a few lines before having a go at it themselves.

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*
Mastermind 2013-11-07 4 on 3 exercise

2) 6 colours on 4 spots**
Mastermind 2013-11-07 6 on 4 exercise

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


Example of sum with 2 pairs of swapped digits
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.