Optional Homework for next session on 5th May (Some were done in class)
 Which of these two are equal?   Rt2 + Rt2 + Rt3, Rt5 + Rt5, Rt3 + Rt8, Rt2 + Rt5 + Rt1.
(Rt2 is the square root of 2)
 
The reverse of a two digit prime number is also prime and differs from it by a square of which integer?
 
 University Challenge question: If the cardinal numbers are written out in order, the first occurance of the letter A is in 101. What number shows the first occurance of the letter B?
 
There are two red, two green and two blue balls, all the same size. For each colour one ball is heavy and one light. All heavy balls are equal in weight and so are all light balls. How many weighings,  using a balance, are required to identify the three heavy balls?
 
 A pool is filled by four taps. On its own tap A will fill the pool in 48 hours. On its own tap B will fill the pool in 72 hours. Likewise tap C takes 96 hours and tap D 6 hours.How long will it take to fill the pool if all four taps are on?
 
 I have three glasses which hold 7, 4 and 3 litres respectively. The 7 litre glass is full of water. How can I get exactly 2 lots of 2 litres of water? There is no tap.
 
 I have four weights with which I can measure any integral weight from 1kg up to 15 kg. I also have a balance. What are the weights?   (Repeat for 40. Repeat for 80.)
 
 An addition Arithmagon has vertex numbers A, B, C and D. If the side are 3, 15, 35 and 7 what are the values of the vertex numbers?
 
A multiplication Arithmagon triangle has sides: -6+2Rt2, 7+7Rt2 and 2-4Rt2.
What are the corner numbers?
 
A certain company has 50 shares which are held by 6 board members.The Managing director plus any two shareholders have a majority of shares. Any 4 shareholderss constitute a majority. Any four board members can hold a majority. How many shares does each of the 6 board members hold?
 
 Find the sum of the series 1/2! + 2/3! + 3/4! + 4/5! +...+ n/(n+1)!   What if n tends to infinity?
 
 1! + 2! + 3! + … + n! Ends in what digit?
 
 There's a toy boat floating in a pool.
Place a lead ball in the boat (without sinking it), and measure the level of water in the pool.
Now take the ball out of the toy boat and drop it into the pool, and measure the water's level again.
Will the two water level measurements be different, if so which will be higher?
 

 What mathematical symbol can be put between 5 and 9 to make a number bigger than 5 and smaller than 9?

 What 5-digit number has the following features:
If we put the numeral 1 at the beginning, we get a number three times smaller than if we put the numeral 1 at the end of the number.