The challenge this week is to switch round the four knights as shown above, using only regular knights chess move (L shape – one along two up/down, or two along one up/down). Two knights can’t occupy the same space so you will need to be careful!
For an interesting discussion of the solution see this video .
Here is probably the hardest puzzle we’ve looked at so far in maths club …
Two perfect logicians, Sam and Polly, are told that integers x and y have been chosen such that 1 < x < y and x+y < 100. Sam is given the value x+y and Polly is given the value xy.
They then have the following conversation.
Polly: I cannot determine the two numbers.
Sam: I knew that.
Polly: Now I can determine them.
Sam: So can I.
Given that the above statements are true, what are the two numbers?
Starting points:
Before Polly and Sam say anything:
What is the range of numbers Sam could be given?
What is the range of numbers Polly could be given?
What special type of number can the product of x and y never be?
What about the square of these numbers?
After Polly’s first statement:
Give two examples of products that Polly can not be given.
After Sam’s first statement:
Give two examples of sum’s that Sam can not be given.
Next steps …
At this point you probably want to start using a computer to generate a list of numbers that they could be given.
This puzzle comes from Alex Bellos’ column in the Guardian. It has been adapted from one by Prem Prakash, an electrical engineer from Bangalore, India, who has taken early retirement to develop puzzle-based teaching workshops.
You and your two friends Pip and Blossom are captured by an evil gang of logicians. In order to gain your freedom, the gang’s chief, Kurt, sets you this fearsome challenge.
The three of you are put in adjacent cells. In each cell is a quantity of apples. Each of you can count the number of apples in your own cell, but not in anyone else’s. You are told that each cell has at least one apple, and at most nine apples, and no two cells have the same number of apples.
The rules of the challenge are as follows: The three of you will ask Kurt a single question each, which he will answer truthfully ‘Yes’ or ‘No’. Every one hears the questions and the answers. He will free you only if one of you tells him the total number of apples in all the cells.
Pip: Is the total an even number?
Kurt: No.
Blossom: Is the total a prime number?
Kurt: No
You have five apples in your cell. What question will you ask?
See here for the solution.
Today we looked at how we can transform a blank sheet of A4 paper into many different shapes such as an equilateral triangle and a kite. To do so you can either try to figure it out yourself or you can follow the Origami instructions for each different shapes.
If you have anymore interesting ideas please share them in the comment section below and if you want an extra challenge try proving that all of these folds actually give regular shapes bearing in mind the fact that the ratio of the sides in an A4 paper is 1:root 2
