Find all the different quadrilaterals you can make by joining four dots on a 9-dot grid.
Different in this case means not congruent – i.e. none of your quadrilaterals should be able to be formed by rotating, translating or reflecting one of your other quadrilaterals.
Here is a couple to get you started:
How many can you find?
Some of these puzzles are taken from a nice book by Alex Bellos called Can you solve my problems? Alex Bellos does a fun puzzle blog on the Guardian every two weeks.
The Four Stacks
Start with eight coins in a row, and create four stacks of two coins in four moves. A move consists of moving one coin to the left or right by hopping over two coins and landing on the third one along. You can hop over single coins or stacks.
Tait’s Teaser
The aim of the puzzle is to start with two different types of coin (or heads and tails of the same coin) in the arrangement above and get to the arrangement below in as few ‘moves’ as possible.
A move consists of moving two adjacent coins at the same time. You can move them anywhere in the same line, but you can’t switch the two coins around as you do so.
The answer is not five!
Frogs and Toads
Place six coins as shown above. The white ones represent toads and the grey ones are frogs. Frogs and toads can only move by hopping over one other frog or toad to an empty space. Toads can move to the right, and frogs to the left. Can you rearrange them into the position below?
See here for an interactive version of this puzzle created by NRich which allows you to change the number of frogs and toads.
Star Puzzle
Draw a star and try to place 9 coins on any of the black vertices. You can place coins by starting from a vertex which is empty, moving in a straight line and counting 1,2,3. Number 1 is the vertex you start on, number 2 may or may not have a coin on it, and number 3 is where you place your coin.
Two possible opening moves are shown below
Here is an attempt that has gone wrong! 7 coins have been placed but there is no way to place any more, because you must start on an empty vertex.
Here is a great little applet coded by Etienne Royer-Gray to play with:
The first challenge today was to cut a square out of a piece of paper using just one straight cut with a pair of scissors.
The picture above gives you a hint how to fold it first if you look closely!
Next challenge is to cut out an equilateral triangle by doing some careful folding and just one straight cut.
Here are instructions for making the letters of your name just using one cut! Click on “Folding Steps” for step by step instructions.
Paper folding and cutting can be taken very far – you can try to make all the number diamond playing cards in this way!!
For hints on this challenge and more activities see this page from the Wild Maths website.
Happy New Year! Hope you enjoyed your extra second before hand! Try this game online aptly called Approaching Midnight.
Then try Got It and Escape Vortex.
You may able to use similar strategies for all three!