Archive for the ‘Puzzles’ Category.

3rd March 2019, 02:31 pm

I’ve been invited to help with the Puzzle Column at the MSRI newsletter *Emissary*. We prepared six puzzles for the Fall 2018 issue.

I love the puzzles there. Number 2 is a mafia puzzle that I suggested. Number 6 is a fun variation on the hat puzzle I wrote a lot about. Here is puzzle Number 3.

**Puzzle.** Let A = {1,2,3,4,5} and let P be the set of all nonempty
subsets of A. A function f from P to A is a “selector” function if f(B)
is in B, and f(B union C) is either equal to f(B) or f(C). How many
selector functions are there?

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2nd February 2019, 02:12 pm

4th January 2019, 11:13 am

14th December 2018, 12:19 pm

Alex Bellos sent me his new book Puzzle Ninja: Pit Your Wits Against The Japanese Puzzle Masters. What has he done to me? I opened the book and couldn’t close it until I solved all the puzzles.

This is a fantastic book. There are many varieties of puzzles, including
some types that I’ve never seen before. Also, the beautifully designed
puzzles are great. Often puzzles of the same type target different
solving ideas or have varied cool themes.

This book is more than a bunch of puzzles; it also contains poetic
stories about puzzle histories and Japanese puzzle designers. Fantastic
puzzles together with a human touch: this might be my favorite puzzle
book.

I present two puzzles from the book. The puzzle type is called *Wolf and Sheep Slitherlink*.
The Slitherlink is a famous puzzle type with the goal of connecting
some of the neighboring dots into a single non-self-intersecting loop. A
number inside a small square cell indicates how many sides of the
square are part of the loop. *Wolf and Sheep Slitherlink* is a variation of *Slitherlink* in which all sheep should be kept inside the fence (loop) and all the wolves outside.

Ignore the numbers in the title as they just indicate the order number
of Wolf and Sheep Slitherlink puzzles in the book. The number of ninja
heads shows the level of difficulty. (The hardest puzzles in the book
have four heads.) The difficulty is followed by the name of the puzzle
master who designed the puzzle.

The first puzzle above is slightly easier than the second. I like the
themes of these two puzzles. In the first one, only one cell—lonely
wolf—marks the relationship to the fence. In the second one, the wolf in
the center—who needs to be outside the fence—is surrounded by a circle
of sheep who are in turn surrounded by a circle of wolves.

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5th December 2018, 12:50 pm

25th September 2018, 04:08 pm

I found this puzzle on the Russian QWERTY channel.

Five people sit around a table playing Mafia. Among them are two innocent people, two Mafiosos, and one detective. The Mafia people know each other; the detective knows who each of them is; and the innocent people have no information whatsoever about anyone at the table.

During this particular game, the innocents and the detective always tell the truth, while mafia people always lie. They start by going around the circle making the following statements:

- A: I know who B is.
- B: I know who the detective is.
- C: I know who B is.
- D: I know who E is.

Who is who?

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29th August 2018, 02:59 pm

My coauthor, Konstantin Knop, sent me a coin-weighing problem that is really good. Surprisingly, it is old: it first appeared in a Russian math journal, *Kvant*, in 1973.

**Puzzle.** At a trial, 14 coins were presented as material evidence. The expert tested the coins and discovered that seven of them were fake, the rest were real, and he knew exactly which coins were fake and which were real. The court only knows that counterfeit coins weigh the same, real coins weigh the same, and fake ones are lighter than real ones. The expert wants to use not more than three weighings on a balance scales without weights to prove to the court that all the counterfeit coins he found are really fake, and the rest are real. Could he do it?

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25th August 2018, 06:29 pm

23rd August 2018, 05:57 pm