maths puzzles

Maths Puzzles

These should all be accessible for top sets in KS4 and post 16. See if you can manage to get all 3 correct.

Puzzle Number 1

Why is x^x undefined when x = 0 ?

Puzzle Number 2

I multiply 3 consecutive integers together. My answer is 8 times the middle of the 3 integers I multiplied. What 3 numbers could I have chosen?

Puzzle Number 3

You play a game as follows:

1 point for a prime number
2 points for an even number
-3 points for a square number

(note if you choose (say) the number 2 you get +1 for being a prime and +2 for being an even number giving a total of 3 points)

You have the numbers 1-9 to choose from. You need to choose 4 numbers such that their score adds to zero. How many different ways can you find to win this game?

Answers below in white text (highlight to reveal)

1) x^x is undefined because using 2 different indices rules will give us contradictory results. 0 to any power will always be 0, however any number to the power 0 will always be 1. With 2 contradictory answers we leave it as undefined!

2) The equation we want is (x)(x+1)(x+2) = 8(x+1). This simplifies to x^3 + 3x^2 -6x – 8 = 0. We can solve this using the factor theorem, polynomial division or by plotting a graph to get 2 possible solutions – x = 2 or x = -4.

3) The numbers will have the following values: 1 = -3, 2 = 3, 3 = 1, 4 = -1, 5 = 1, 6 = 2, 7 = 1, 8 = 2, 9 = -3. There are at least the following possible combinations:
1,2,3,4
1,2,5,4
1,2,7,4
9,2,3,4
9,2,5,4
9,2,7,4
6,8,4,9
6,8,4,1
Check to see I haven’t missed any!

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