Mastermind is a game played by two players, the codemaker and the codebreaker.

http://www.cut-the-knot.org/Curriculum/Games/MastermindVariant.shtml
Below is one simulation you may try on your computer. For simplicity, I do not hide goats behind the doors. There is only one 'abstract' prize

http://www.cut-the-knot.org/hall.shtml
You only have to press one of the buttons, "Yes" or "No". This is how you play.

http://www.cut-the-knot.org/Curriculum/Algebra/Cards.shtml
Peg Solitaire (also known as Hi-Q) has very simple rules. Pegs (red circles in this implementation) are allowed to jump over adjacent (vertically or horizontally) pegs.

http://www.cut-the-knot.org/proofs/pegsolitaire.shtml
The purpose of the applet below is to demonstrate how Riemann sums approximate the value of a definite integral.

http://www.cut-the-knot.org/Curriculum/Calculus/RiemannSums.shtml
The Mean Value Theorem (MVT, for short) is one of the most frequent subjects in mathematics education literature.

http://www.cut-the-knot.org/Curriculum/Calculus/MVT.shtml
According to one story [Kasner, p. 159], Siméon Denis Poisson, one of the greatest mathematicians of the 19th century, owed his interest in mathematics to a chance encounter with a simple problem

http://www.cut-the-knot.org/ctk/Water.shtml
The Toads And Frogs Puzzle is also known under the names of Hares and Tortoise and Sheep and Goats. With no animals at hand, it can be played with two kinds of coins.

http://www.cut-the-knot.org/SimpleGames/FrogsAndToads.shtml
Here's a 2-dimensional variant of the Toads and Frogs puzzle. The rules are virtually identical. Frogs only move rightward or downward, toads can only move leftward and upward.

http://www.cut-the-knot.org/SimpleGames/FrogsAndToads2d.shtml
We are given a tower of eight disks (initially four in the applet below), initially stacked in increasing size on one of three pegs.

http://www.cut-the-knot.org/recurrence/hanoi.shtml