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Off-Topic Discussion => General Discussion => Topic started by: GhylTarvoke on December 22, 2016, 04:08:02 am

Title: Favorite Puzzles
Post by: GhylTarvoke on December 22, 2016, 04:08:02 am
What are your favorite puzzles? Here are some of mine, in no particular order:
Puzzle #1 (Riddle)

Left alone, I'm a word with five letters.
I'm honest and fair, I'll admit.
Rearranged, I'm of no use to trains.
Again, and I'm an overt place, warm and well-lit.
Puzzle #2 (Arithmetic)

Get 24 by combining parentheses, addition, subtraction, multiplication, division (but not necessarily all of those operations), and all four of these numbers: 3, 3, 8, 8.
Puzzle #3 (River Crossing)

Four people (A, B, C, and D) must cross a bridge at night.

The bridge can only carry two people at once.
There is only one flashlight, which must be used while crossing the bridge.
A can cross in 1 minute. B can cross in 2 minutes. C can cross in 5 minutes. D can cross in 8 minutes.
When two people cross the bridge together, they must move at the slower person's speed.

Can all four people cross the bridge in 15 minutes?
Puzzle #4 (Maze)

(http://4.bp.blogspot.com/_ZrYtgXFkqME/R8zZXvDvkkI/AAAAAAAAAD4/ZCemrK2zQE0/s1600/smallfractalmaze.gif)

The paths are colored for convenience only. Boxes A, B, and C are identical to the entire maze, so the maze has infinite depth.
Start at the minus sign on the topmost level. Your goal is to reach the plus sign on the topmost level.
Puzzle #5 (Precalculus)

Take n equally spaced points on the unit circle. Call one of the points P. Draw chords from P to the other n - 1 points. What's the product of the chord lengths?
Puzzle #6 (Physics)

There are b black balls and w white balls in a straight line, with black balls on the left and white balls on the right.
The black balls roll to the right at a constant speed. The white balls roll to the left at the same constant speed.
At the start, no two balls are touching. Assume that collisions are perfectly elastic. How many collisions will there be?
Puzzle #7 (Chess)

(https://1.bp.blogspot.com/_yI5fmfDFGUc/SC_f7cNg9MI/AAAAAAAAAWc/4jpcsg7wYfs/s1600/ncp00115.jpg)

White to move and win.
Title: Re: Favorite Puzzles
Post by: Ghostavo on December 22, 2016, 04:26:55 am
This puzzle is one of my favorite for showing students the beauty of breakthroughs.

(http://www.jinchess.com/chessboard/?p=-----------k--------------Kp-p-p---Pp-p-----P-P------PP---------)

Black to move.
Title: Re: Favorite Puzzles
Post by: GhylTarvoke on December 22, 2016, 05:28:47 am
Aha! I didn't think it was possible at first.

Spoiler:
Assuming White doesn't play f3: 1...f4, then 2...h4, then 3...h3 if possible, or 3...g3 otherwise.
Title: Re: Favorite Puzzles
Post by: Ghostavo on December 22, 2016, 01:34:31 pm
My favorite line is

Spoiler:
1...f4 2.Kxd5 h4 3.Kxe4 and now the beautiful 3...f3! stopping White's king from catching the h pawn if taken.
Title: Re: Favorite Puzzles
Post by: GhylTarvoke on December 22, 2016, 01:53:52 pm
Oh, I missed that line. Yes, it's beautiful.