City of Truths

Imagine you are on planet Trulie with only two inhabitants, one that always tells the truth, and the other that always lies. You reach a fork in the road with a sign to the City of Truths. Unfortunately, the road sign is down. Fortunately, a Trulian appears from nowhere. What question do you ask him to find the way to the City of Truth?

Adaptation of Doctor Spacemath from:
Fractals, Googols, and Other Mathematical Tales by Theoni Pappas

Wolf, Goat, and Cabbage

The Moscow Puzzles: 359 Mathematical Recreations (Math & Logic Puzzles)
by Boris Kordemsky

This problem can be found in eighth-century writings:

A man has to take a wolf, a goat, and some cabbage across a river. His rowboat can only hold the man plus either the wolf, the goat, or the cabbage. If he takes the cabbage with him, the wolf will eat the goat. If he takes the wolf, the goat will eat the cabbage. Only when the man is present are the goat and the cabbage safe from their enemies. All the same the man carries wolf, goat, and cabbage across the river. How?

mathcats variant:
Crossing the River (with a Wolf, a Goat, and a Cabbage) :

Sailor Cat needs to bring a wolf, a goat, and a cabbage across the river.
The boat is tiny and can only carry one passenger at a time.
If he leaves the wolf and the goat alone together, the wolf will eat the goat.
If he leaves the goat and the cabbage alone together, the goat will eat the cabbage.
How can he bring all three safely across the river?

Erich Prisner: Wolf, goat, cabbage, … applet+setup
Lulu’s games: The wolf, the goat, and the cabbage
Cut the Knot: Goat, Cabbage and Wolf applet

One at a Time

Fractals, Googols, and Other Mathematical Tales

by Theoni Pappas

Fractals, Googols, and Other Mathematical Tales by Theoni Pappas

What’s Math Got to Do with It?

How Parents and Teachers Can Help Children Learn to Love Their Least Favorite Subject by Jo Boaler

In Code

A Mathematical Journey, by Sarah Flannery