Clean interactive quizzes aiming to develop students' curiosity and problem solving skills.

- Introduction
- Existence proofs
- Cutting a figure into two equal parts
- Splitting weights

- How to find an example?
- Magic square with 1, 2, 3, 4, 5, 6, 7, 8, 9
- Multiplicative magic square with different positive integer
- Paying 5 florins via 7- and 13-florin coins
- 3 hotels

- Computer search
- Optimality
- Recursion
- Hanoi towers
- Largest amount impayable with given coin types
- Two cells of opposite colors

- Induction
- Examples, counterexamples, logic
- For every integer n>1 the number n^2+n+41 is prime?

- Reduction ad absurdum and pigeon hole principle
- 30 candies
- Put numbers 1..64 on the chessboard in such a way that neighbors (common side) differ at most by 4
- put 10 integers around a circle in such a way that each of them is an arithmetic mean of its two neighbors, and not all numbers are the same
- is it possible to put numbers 1 2 3 4 5 6 7 8 around the circle in such a way that (a) sum of any two neighbors is odd; (b) sum of neighbors is even; (c) the same question for 1 2 3 4 5 6 7 and odd sum; (d) for 1 2 3 4 5 6 7 and even sum

- Invariants, double counting, termination
- Even and odd numbers and permutations
- Pieces on chessboard.
- a turtle is going forward one unit, then turns right or left (by 90 degrees), moves one unit, turns again etc. Can it return to original position after 15/16/17/18 moves?
- is it possible to place signs in the expression 129 to get result 0? 1? 2? 100?
- there are 5 objects in a row labeled a,b,c,d,e,f. The goal is to put them in a different order using given number of transpositions (by mouse?), or declare that this is not possible. Two configurations that should be achieved by 20/21 transpositions (if this is not possible, this should be declared).
- the same as previous but only transposition of neighbors are allowed. (One of the required permutations is a transposition of two non-neighbor elements.)

- Project: 15-game

to be written

- Introduction