We’re delighted to announce the winners of our fifth set of Pre-GCSE Inspire competitions! For Class 5 we built on Class 1’s focus on Maths by looking at games like the Game of Life and Tetris. In the competitions, students had the chance to tackle some tricky Maths-based games; you can find the answer guides to the questions below, as well as a selection of the excellent entries we received!
Congratulations to the winners of Class 5 competitions:
- Adchaya, Ealing
- Georgia, Ealing
- Rebecca, Harrow
- Sarah, Harrow
- Raya, Ealing
- Thomas, Ealing
Each of you have won an Amazon voucher. This will be sent to the email address you provided in your competition cover sheet; please get in touch with us at firstname.lastname@example.org if you haven’t received yours by the end of the week.
Competition 12: A Tetris puzzle
One of the most successful video games of all time is Tetris. There are seven different Tetris pieces: the long piece, the square, the T-piece, two L-pieces and two Z-pieces. Each piece is made up of four square blocks, and in fact the name of the game comes from the Greek prefix tetra meaning ‘four’.
Suppose you are given exactly one of each of the seven different Tetris pieces. Is it possible to arrange them in such a way that they form a 4 × 7 rectangle?
Your competition entry should explain how you reached your answer in no more than 300 words, and may involve illustrations.
1st place: Adchaya, Ealing
2nd place: Georgia, Ealing
- Aaqib, Harrow
- Charlize, Ealing
- Imana, Harrow
- Sarah, Harrow
Competition 13: Poisonous chocolate
1st place: Rebecca, Harrow
2nd place: Sarah, Harrow
1) If there is a 3×3 bar of chocolate, I would want to go second, as whoever goes first when m=n, gets the poisonous piece. This is also shown when playing with the 2×2. This is not only for 2×2 or 3×3, anytime m=n, the second player will always win. The logic for this is that a 1×1 chocolate is poisoned, and anytime the m is equal to n, the number of turns between the players will always be even, therefore the first player will always end up with the poisoned chocolate as the second player will always have the last choice.
2)a: If I have a 3×5 bar of chocolate, I would want to go second because there are two more columns than there are rows so the overall number of turns are still even and the first player will always lose. Based on this we can tell that when both m and n are odd numbers, and also when m and n are both even numbers then the second player will always win as they will have the last choice and the first player will be left with the poisoned chocolate. The position of the poisoned piece is irrelevant because ultimately the number of turns remains the same.
b) The choice of being first or second player always depends on the number of turns the players will have. Keeping this in mind, when the difference between n and m is an even number, the second player will always win as there are an even number of turns to break the chocolate, always leaving the first player with the poisoned piece.
In this same way when m is even and n is odd or vice versa then the first player will always win as there will be an odd number of turns and the second player will be left with the poisoned chocolate.
There will always be (n+m-1) number of turns until only the poisoned piece is left.
Since 3 is an odd number, if n>5 is an even number such as 6 or 8 then the first player would win as the number of turns would be odd however if n>5 is an odd number then the second player would win as the number of turns would be even.
3) The second player would win because no matter what m is equal to, n is 2 more than m which means that there will be an even number of turns and therefore the first player will end up with the poisonous chocolate. The difference here between m and n is 2 which is an even number and this relates back to the rule mentioned in answer 2.
- Georgia, Ealing
Competition 14: The game of life
Each class will have a photo, art or short video competition with a prompt based on the topic we are studying in that class. For this glass, the competition is based on the Game of Life: after listening to Dr Tom Crawford’s explanation of the Game of Life, you can do some of your own experimenting with the game here. See if you can design a starting pattern and predict what the game will do with it.
Your competition entry should be a photograph or screencap of your starting pattern, or a short (<10 seconds) video of your game in action. You should also include a short written explanation (maximum 100 words) in which you explain what you expect to happen in your game.
1st place: Raya, Ealing
2nd place: Thomas, Ealing
Remember: the deadline for Class 6’s competitions is 5pm next Wednesday, 22 July. This is the final online class for this academic year and we’re looking forward to seeing some more fantastic work – and there are some more Amazon vouchers on offer for the winning entries!