# Theory

Hockey Stick Identity - Yr 11+. WORK IN PROGRESS - MESSY!

# Questions

How many numbers have this property? - Yr 5+. Divisibility by 5 test, familiarity with counting/arrangements.

Number square - Yr 7+. Knowledge of averages leads to one possible approach, but not necessary - can be solved with basic reasoning.

Dice problem - symmetry shortcut - Yr 7+. Best to have some familiarity with dice problems already.

Symmetry vs counting outcomes - Yr 7+. Nice introduction to symmetry techniques by way of comparison with basic methods. Dice problem.

Jellybean problem - Yr 7+. With/without replacement.

Scheduling problem - Yr 7+. Factorial notation nice but not necessary.

Pigeonhole principle problems - Yr 7+.

Frog puzzle - Yr 7+. Knowledge of the coordinate grid and basic probability.

3 perspectives on a seating problem - Yr 7+. Familiarity with seating problems helpful, factorial notation nice but not necessary. Example of symmetry technique.

A variety of problems - Yr 7+. Basic probability, expected value, some involve algebra.

The Principle of Inclusion/Exclusion questions - Yr 7+. Some require algebra.

Mostly expected value plus some quick questions on other topics - Yr 7+. Variety of questions from easy to tough.

How many triangles can we make? - Yr 7+.

Sum of the 5-digit palindromes - Yr 7+. Multi-part.

Probability that a sum is divisible by 3 - Yr 7+. Familiar with mod helps.

Length questions - Yr 7+. Probability that a point falls within a certain interval.

Area questions - Yr 8+. Probability that point/s fall within a certain area.

Arrival times - Yr 9+. Requires coordinate geometry.

Coordinate geometry probability questions - Yr 9+. Probability that a point is within a certain region of the plane.

Odd or even? - Yr 9+.

Location in the plane - Yr 9+. Probability of being closer to one point than another.

Arranging books - Yr 10+. Factorial notation helpful. Best to have some familiarity with simpler arrangement problems.

Seating plan question - Yr 10+. Factorial notation helpful. Best to have some familiarity with simpler arrangement problems.

Probability of a point being inside a region - Yr 10+. Area of a circle, circles in the coordinate plane.

Grid problems - Yr 10+. How many possible paths through a grid?

Somewhat unusual nC4r problems - Yr 10+.

Picking squares on a grid - Yr 10+. Knowledge nCr notation.

Two probability questions - Yr 10+. 1: nCr notation, binomial distribution. 2: dice and coins problem.

Problem using the method of 1-1 correspondences - Yr 11+. Uses nCr notation.

Distributing n items to k boxes - Yr 11+. Uses nCr notation.

Problems using Fibonacci - Yr 11+.