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 xx 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) xx 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:
Check to see I haven’t missed any!
If you like this post, you might also like:
A Maths Snooker Puzzle. A great little puzzle which tests logic skills.
Visualising Algebra Through Geometry. How to use geometry to simplify puzzles