383.—­THE “T” CARD PUZZLE.

[Illustration]

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?

384.—­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 is 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.

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385.—­“STRAND” PATIENCE.

The idea for this came to me when considering the game of Patience that I gave in the Strand Magazine for December, 1910, which has been reprinted in Ernest Bergholt’s Second Book of Patience Games, under the new name of “King Albert.”

Make two piles of cards as follows:  9 D, 8 S, 7 D, 6 S, 5 D, 4 S, 3 D, 2 S, 1 D, and 9 H, 8 C, 7 H, 6 C, 5 H, 4 C, 3 H, 2 C, 1 H, with the 9 of diamonds at the bottom of one pile and the 9 of hearts at the bottom of the other.  The point is to exchange the spades with the clubs, so that the diamonds and clubs are still in numerical order in one pile and the hearts and spades in the other.  There are four vacant spaces in addition to the two spaces occupied by the piles, and any card may be laid on a space, but a card can only be laid on another of the next higher value—­an ace on a two, a two on a three, and so on.  Patience is required to discover the shortest way of doing this.  When there are four vacant spaces you can pile four cards in seven moves, with only three spaces you can pile them in nine moves, and with two spaces you cannot pile more than two cards.  When you have a grasp of these and similar facts you will be able to remove a number of cards bodily and write down 7, 9, or whatever the number of moves may be.  The gradual shortening of play is fascinating, and first attempts are surprisingly lengthy.