Futility Closet

A Martian sand lizard can reproduce itself in a single day. Start with a single sand lizard and on succeeding days you'll have 2, then 4, and so on. In 30 days you'll have 536,870,912 lizards.

How long would it take to reach that number if you started with two lizards? I'll give the answer tomorrow.

Solution to The Scissors Entangled, from Monday:

"The scissors may be released by drawing the noose upwards through the eye of the scissors, and passing it completely over them."

From Dick & Fitzgerald, The Book of 500 Curious Puzzles, 1859.

"An old but a capital puzzle." How can you extricate the scissors from the twine?

I'll give the answer tomorrow.

Solution to Steadfast, from Thursday:

1. Nd3 Ka3 2. Nb1+ Ka2 3. Kf1 Ka1 4. Nc3#

By W. Bone. White to move and mate in four.

The catch: He must mate with the queen — and she's glued to the board.

I'll give the solution tomorrow.

Solution to Measuring the River, from Sunday:

"Measure any convenient distance along the bank from A. to C, say 40 yards. Then measure any distance perpendicularly to D, say 12 yards. Now sight along DB and find the point E. You can then measure the distance from A to E, which will here be 24 yards, and from E to C, which will be 16 yards. Now AB:DC = AE:EC, from which it is evident that AB, the width of the river, must be 18 yards."

A traveler reaches a river at the point A and wishes to know the width across to B. As he has no means of crossing the river, what is the easiest way of finding its width?

From Henry Dudeney. I'll give the answer tomorrow.

Solution to Cryptic Addition, from Tuesday:

"If you turn the page upside down you will find that one, nine, one, and eight added together correctly make nineteen."

From Henry Ernest Dudeney. Can you prove that this sum is correct?

I'll give the explanation tomorrow.

Solution to Fire Escape, from Saturday:

Accept the challenge. Wait for Nimzowitsch's first move, and then play that move on Alekhine's board. When Alekhine responds, copy his move on Nimzowitsch's board. In effect the two masters are playing against one another; you're just transferring the moves between them. Since their game must end in a win or a draw, you're guaranteed to escape hell. You don't even have to know how to play chess!