Futility Closet

Solution to War, from Tuesday:

1. Nc5+ Kc4+ 2. Bb3+ Rxb3+ 3. axb3+ Qxb3+ 4. Qxb3#

By Charles Tomlinson. White to play and mate in 4 moves, giving check on every move and forcing Black to do the same.

I'll give the solution tomorrow.

Solution to Lightning Addition, from Sunday:

Gauss included 0 in the series and rearranged the terms into 50 pairs, each of which totals 100:

100 + 0
99 + 1
98 + 2
etc.

The 50 pairs together make 5000, which, when added to the unpaired central number, 50, gives 5050, the correct sum.

A (probably apocryphal) story tells that, as a 10-year-old schoolboy, Carl Friedrich Gauss was asked to find the sum of the first 100 integers. The tyrannical schoolmaster, who had intended this task to occupy the boy for some time, was astonished when Gauss presented the correct answer, 5050, almost immediately.

How did Gauss find it? I'll give the answer tomorrow.

Solution to There Goes the Neighborhood, from Saturday:

It would take 29 days. Essentially you'd be starting from day 2 in the original example.

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.