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

“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

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.

Pattern code – chemistry

1) Graphs
What code goes to the question mark?

You can check your solution>here

 

A new puzzle is published every friday. The solution is generally published one week later. I welcome your reactions on these puzzles: are they too easy, too difficult, are there any multiple solutions? How long did you need to solve it?

Eleusis

Yes, I know my slogan is “just puzzles”. So I shouldn’t be writing about games. Having said that, let me first explain the game of Eleusis before proceeding to the puzzles.

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 playes 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.

Example:

In this sample game, the Rule Inventor played Ace of diamnonds and 2 of Hearts. The first player played 3 of diamonds, which the Rule inventor turned down. The second player played Jack of diamonds, which turned out to be also incorrect. The 3rd player tried 3 of clubs, which the Rule Inventor added to the top row. The next two cards played were a 9 of hearts and a 10 of diamonds, which the Rule Inventor both declared to be wrong. The last card played was the Ace of spades.

Now here is a rule to find out.
1) Rule 1^*


In your hand you have:


Which of them do you play? And why?

2) Rule 2^**


In your hand you have:


Which of them do you play? And why?

In the explantion of the game above I omitted 2 complications:
– if the player thinks he can not play a valid card, he may claim this and exchange his hand. If he is right, he exchanges his hand for a hand with one card less from the deck. If he is wrong, the RuleInventor plays a correct card and the player draws two cards from the deck.
– if a player thinks he knows the secret rule, he may declare himself prophet. The prophet now first judges all cards played, before the Rule Inventor. If he keeps his job till the end of the game, he wins the game instead of the player who first gets rid of all his cards.

Though I am out of touch with him now, I have very good memories of my correspondence with him about two decades ago, and he is a very kind man.

As usual, you are welcome to report your solution times and comment on the solution, but please do not give away the answer – that may spoil the fun for others. I will publish the solution in one or two weeks after posting the puzzle.

You can check your solution here and

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New puzzles are published every Friday, at which time also the solution to the previous weeks puzzle is published.

You can expect more Eleusis based puzzles in one of the upcoming free e-books.

Incidentally, this is the 100th post on this blog. The game Eleusis is an old favourite of mine, and thus a worthy subject of this celebration.

Inspector Simon Mart back in London

Back in London, Inspector Simon Mart of Scotland Yard looked at the interrogation reports before him. All three were known criminals, and now suspected of a VST, a Very Serious Theft. In fact, nothing less than the miniature of the royal train carriage had been stolen from the Toy Museum.

It had already been proved that one, and no more than one of them, had stolen the miniature train carriage.

Andy: Billy did it. Charles is innocent.
Billy: Charles did it. Everything Andy says is a lie.
Unfortunately, Charles two statement were in London slang that was totally incomprehensible even to inspector Mart.

1) Billy^*
The officer in charge first wanted to know if Billy could be released – Billy’s lawyer had filed an urgent request that Billy would be allowed to visit his sick mouse in animal hospital.
Suppose Billy is guilty. Then A1 is T, A2 is T. Hence Billy is innocent.

2) Whodunnit?^*
Next of course came the question: Who had done it?

3) The three girls^*
Inspector Simon Mart looked at the next interrogation report. Another VST case, he concluded, and he took a fresh cup of chocolate milk to prepare himself.
Denise, Ellen and Felice had been at the party given by the young Duchess Ginaldino. At the end of the evening, when all three guests had left, it turned out that Ginaldino’s favourite doll, Helen, had been stolen. It was clear that one of the three visitors was the culprit. Young as the three girls were, they were so spoiled that non of them could speak three sentences without lying at least once.

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.

Dissections – the Greek cross

The Greek cross consists of 5 squares joined in the shape of a cross.

1) Greek cross – 4 equal parts^*

The figure above shows a strangely formed meadow between a brook and mountains. There are 4 wells in the area. The farmer died and stipulated in his will that his land would be distrubuted equally among his 4 sons; all 4 lots would have the same area and shape and contain exactly 1 well.

How was the land divided among the 4 sons?

2) The hindu problem

The greek cross as shown in the illustration to the left, is composed of 5 equal sized squares. Cut the cross into five pieces to form a square. There are 2 solutions. According to British puzzle master Henry Dudeney, the problem is over 3000 years old.

3) How many straight cuts?
Henry Dudeney next comes up with the problem:
How many cuts do you need to divide the Greek cross into 4 pieces, so that with these pieces you can form a square?

4) The Red CRoss Lassie
American puzzle master Sam Loyd recounts the following problem:

In the whole realm of puzzledom, and geometry included, there is nothing so fascinating and eminanetly scientific as the series of problems pertaining to the form of the Greek cross and its peculiar relations to the square, parallelograms and other symmmetrical shapes.
As differing from the well known mathematical problem of converting the cross into a square by the fewest possible number of cuts, attention is called to the following pretty feat of chaninging one cross into two.
It appears that one of our wounded boys in blue who was returning home after being nursed back to life by a faithful Red Cross lassie, begged the red cross from her arm as a keepsake; but she, in true sweetheart style, took her scissors and by a few deft clips, cut the red cross into several pieces, which could be fitted together perfectly so as to make two crosses of similar vsize. It is a simple but beautiful trick, and the satisfaction of guessing it will be as great as if you should win a prize.

You can check your solution here for no 1, here for no 2 and here for no 3, and here for no 4

A new puzzle is published every friday. The solution is generally published one week later. I welcome your reactions on these puzzles: are they too easy, too difficult, are there any multiple solutions? How long did you need to solve it?

Cross out

1) Cross out 5×5^**
In the square below, cross out numbers until the sum is 15 in every row and column:

2) Cross out 7×7^**
In the following square, cross out numbers till you the sum is 15 in every row and column:

This type of puzzle was probably invented by Rita Hovestad or Marenke Wiersma, editors of Sanders Brainteaser no 5.

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

A new puzzle is published every friday. The solution is generally published one week later. I welcome your reactions on these puzzles: are they too easy, too difficult, are trhere any multiple solutions? How long did you need to solve it?

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.

E-book number puzzles

Today I proudly present our first free e-book!

This e-book contains 30 unique number puzzles. The puzzles range from brainteasers to futoshiki puzzles and matchsticks problems. Some puzzle types have been published on this blog, others are new.

You can download this e-book here

Matchsticks – make 3 squares

1) Make 3 squares^*

Move 2 matches to make 3 squares of equal size.

This problem comes from J.A.H. Hunter

You can check your solution here

Did you know?
Recent research shows that learning new skills keeps an aging mind sharp.
Lead researcher Denise Park of the University of Texas:
It seems it is not enough just to get out and do something—it is important to get out and do something that is unfamiliar and mentally challenging, and that provides broad stimulation mentally and socially. When you are inside your comfort zone you may be outside of the enhancement zone.

Surgeon

On a dark night a car with 2 people raced along a narrow road. Heavy rainfall left the driver with bad visibility, and the card crashed against a tree when the driver lost control.
Police quickly discovered that the father was dead, but the passenger, his son, was still alive though injured and in critical condition. An ambulance raced the son to the hospital. The surgeon, seeing the patient, cried out:
“Oh no, he is my son!”

Explain.

As always, you are welcome to post your solution times.

If you solved it, you can check your solution