Category Archives: Playing cards

Playing card puzzles by Henry Dudeney

November 15, 2019Playing cardsTeun Spaans

For the past couple of months, I have been publishing puzzles with playing cards. Henry Dudeney was British formost puzzle master of the late 19th / early 20th century. In this series his puzzles, as published in “Amusement in mathematics”, may not be omitted.

1) The card frame puzzle^***/*****
In the illustration we have a frame constructed from the ten playing cards, ace to ten of diamonds. The children who made it wanted the pips on all four sides to add up alike, but they failed in their attempt and gave it up as impossible. It will be seen that the pips in the top row, the bottom row, and the left-hand side all add up 14, but the right-hand side sums to 23. Now, what they were trying to do is quite possible. Can you rearrange the ten cards in the same formation so that all four sides shall add up alike? Of course they need not add up 14, but any number you choose to select.

You can check your solution here

2) The cross of cards^***/*****

In this case we use only nine cards—the ace to nine of diamonds. The puzzle is to arrange them in the form of a cross, exactly in the way shown in the illustration, so that the pips in the vertical bar and in the horizontal bar add up alike. In the example given it will be found that both directions add up 23. What I want to know is, how many different ways are there of rearranging the cards in order to bring about this result? It will be seen that, without affecting the solution, we may exchange the 5 with the 6, the 5 with the 7, the 8 with the 3, and so on. Also we may make the horizontal and the vertical bars change places. But such obvious manipulations as these are not to be regarded as different solutions. They are all mere variations of one fundamental solution. Now, how many of these fundamentally different solutions are there? The pips need not, of course, always add up 23.

You can check your solution here

3) The “T” card puzzle^***/*****

An entertaining little puzzle with cards is to take the nine cards of a suit, from ace to nine inclusive, and arrange them in the form of the letter “T,” as shown in the illustration, so that the pips in the horizontal line shall count the same as those in the column. In the example given they add up twenty-three both ways. Now, it is quite easy to get a single correct arrangement. The puzzle is to discover in just how many different ways it may be done. Though the number is high, the solution is not really difficult if we attack the puzzle in the right manner. The reverse way obtained by reflecting the illustration in a mirror we will not count as different, but all other changes in the relative positions of the cards will here count. How many different ways are there?

You can check your solution here

4) Card triangles^***/*****
Here you pick out the nine cards, ace to nine of diamonds, and arrange them in the form of a triangle, exactly as shown in the illustration, so that the pips add up the same on the three sides. In the example given it will be seen that they sum to 20 on each side, but the particular number is of no importance so long as it is the same on all three sides. The puzzle Pg 116is to find out in just how many different ways this can be done.

If you simply turn the cards round so that one of the other two sides is nearest to you this will not count as different, for the order will be the same. Also, if you make the 4, 9, 5 change places with the 7, 3, 8, and at the same time exchange the 1 and the 6, it will not be different. But if you only change the 1 and the 6 it will be different, because the order round the triangle is not the same. This explanation will prevent any doubt arising as to the conditions.

You can check your solution here

Playing card puzzles (4)

October 18, 2019Playing cardsTeun Spaans

1) A 5×5 grid^***/*****
Which of the 5 cards on the right should take the place of the card turned down?

You can check your solution here

New puzzles are published at least twice a month on Fridays. 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.

Playing card puzzles (3)

August 30, 2019Playing cardsTeun Spaans

This is the third post with puzzles about playing cards.

1) Which hands are valid?^****/*****
In a game, the following six hands are valid plays:

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Which of the following three hands is / are valid?

You can check your solution here

Playing card puzzles (2)

August 16, 2019Playing cards, Recreational mathematicsTeun Spaans

Last month I published two puzzles with playing cards. Here are two more in the same line:

For those who missed the puzzles, look at the figure below. It shows 16 cards, one of which is hidden. At the bottom you find 4 cards. Which of those 4 cards should replace the hidden card?

3) Playing cards puzzle 3^***/*****

You can check your solution here

4) Playing cards puzzle 4^***/*****

You can check your solution here

Playing card puzzles (1)

July 19, 2019Logic, Playing cards, Recreational mathematicsTeun Spaans

While waiting for my appointment with the dentist I thumbed through the magazines, looking for good puzzles. I had little hope of finding any more than a crossword or sudoku, but to my surprise I encountered a new format in the magazine plusonline. The magazine does have a website, as the name suggests, but I couldn’t find the puzzles there.

In all puzzles the problem is: which of the four cards at the bottom should replace the blue card?

Here are two puzzles in the same vein. I did make a small change: the original puzzle had rows of three cards, which I changed into cards rows of four cards.

1) Playing cards square nr 1^***/*****

You can check your solution here

2) Playing cards square nr 2^***/*****

You can check your solution here

Be prepared for more puzzles of this type in a few weeks.

Eleusis

December 6, 2013Inductive reasoning, Playing cardsEleusis, Robert AbbottTeun Spaans

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

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.