Futility Closet

Solution to The Mail Plane:

The motorcyclist would have taken 20 minutes to go from where he met the horseman to the airport and back. Thus he was 10 minutes from the airport when he met the horseman. These 10 minutes plus the 30 minutes the horseman had been riding before they met makes 40 minutes the plane was ahead of schedule.

From B.A. Kordemsky, The Moscow Puzzles, 1956.

A motorcyclist was sent by the post office to meet a plane at the airport.

The plane landed ahead of schedule, and its mail was taken toward the post office by horse. After half an hour the horseman met the motorcyclist on the road and gave him the mail.

The motorcyclist returned to the post office 20 minutes before he was expected.

How many minutes early did the plane land?

(Solution)

Solution to A Geometry Problem:

A shoe.

Don’t blame me.

From Rational Amusements for Winter Evenings, by John Jackson, “private teacher of the mathematics.”

A poser from 1821:

Mathematicians affirm that of all bodies contained under the same superficies, a sphere is the most capacious: But they have never considered the amazing capaciousness of a body, the name of which is now required, of which it may be truly affirmed, that supposing its greatest length 9 inches, greatest breadth 4 inches, and greatest depth 3 inches, yet under these dimensions it contains a solid foot?

What is this body?

(Answer)

Solution to “The Card Challenge”:

Cut the card as shown and it can be drawn out into an endless chain, with an opening large enough for a man to pass it over his body. “A thin person could use a much smaller card.” From Houdini’s Paper Magic, 1922.

A problem posed by Harry Houdini: Given a piece of cardboard measuring 4″ × 2.5″, cut it so that a person can pass completely through it without tearing it.

Can it be done?

(Solution)

Solution to “A Crime Story”:

Theo is innocent because he says so twice. Then (9) is a lie. Since (9) is a lie, (8) is true. Since (8) is true, (15) is a lie. Since (15) is a lie, (14) is true. Judy is the thief.

From the American journal Scripta Mathematica:

An elementary school teacher in New York state had her purse stolen. The thief had to be Lilian, Judy, David, Theo, or Margaret. When questioned, each child made three statements:

Lilian:
(1) I didn’t take the purse.
(2) I have never in my life stolen anything.
(3) Theo did it.

Judy:
(4) I didn’t take the purse.
(5) My daddy is rich enough, and I have a purse of my own.
(6) Margaret knows who did it.

David:
(7) I didn’t take the purse.
(8) I didn’t know Margaret before I enrolled in this school.
(9) Theo did it.

Theo:
(10) I am not guilty.
(11) Margaret did it.
(12) Lillian is lying when she says I stole the purse.

Margaret:
(13) I didn’t take the teacher’s purse.
(14) Judy is guilty.
(15) David can vouch for me because he has known me since I was born.

Later, each child admitted that two of his statements were true and one was false. Assuming this is true, who stole the purse?

(Solution)

Solution to A Riding Tour:

No. A knight lands on light and dark squares alternately. If it begins on a dark square and makes 63 moves, then the last move must end on a light square. h8 is dark. Therefore the task is impossible.

Is it possible to move the knight from a1 to h8, visiting every square of the chessboard once?

(Answer)