1. How many possible opening moves are there for each player in a game of draughts or checkers?
2. What is the next number in this mathematical sequence: 18, 20, 24, 32, ___
3. What is the square root of (a) 121? (b) 12321? (c) 1234321?
4. What is the maximum number of Friday the 13ths possible in one calendar year, including leap years?
5. How many sheets of A4 paper are necessary to cover an A1 sheet?
6. Let’s say you have a garden. On day one, there is only one weed. If the number of weeds doubles every day, and the garden is full of weeds on the 30th day, how many days will it take to fill the garden if we start with two weeds?
7. The year 2013 consisted of four different digits in no particular order. In what year did that most recently occur previous to 2013?
8. The year 2013 also consisted of four consecutive digits in no particular order. In what year did that most recently occur previous to 2013?
9. In the game of Mastermind, a board is sectioned off into rows, each row having four slots in which pegs can be inserted. There are 6 different colours of pegs: green, red, yellow, brown, dark-blue, light-blue. Player (A) makes up some arrangement of four pegs along a row; Player (B) tries to guess what this arrangement is. For every guess that B makes, A responds by putting black and/or white keypegs right next to A’s guess; as follows:
Black keypeg = one of B’s pegs is the correct colour and in the correct position
White keypeg = one of B’s pegs is the correct colour but in the wrong position
So if B manages to guess all four colours and positions correctly, A will respond with four black keypegs, and the game is over.
Here’s a completed game of Mastermind.
B was able to determine A’s arrangement using only five guesses. What’s is A’s arrangement? (State the four colours, left to right)
10. A solid, four centimetre cube of wood is coated with paint on all six faces; then the cube is cut into smaller one centimetre cubes.
These new one-centimetre cubes will have either three painted faces, two painted faces, one painted face, or no painted faces.
a. How many of the cubes will have three painted faces?
b. How many of the cubes will have two painted faces?
c. How many of the cubes will have one painted face?
d. How many of the cubes will have no painted faces?