1. If Kate starts on the paving stone outside her house and hops onto every second stone, she will get to the second to last stone before the house of her friend Sam.
If Kate now turns round on this stone and hops onto every third stone, she will get back to the third stone.
Kate turns back on the third stone and now jumps onto every fifth stone. She finished on the last stone outside Sam's house
(i) Explain why the number or paving stones between the two houses
(a) is an even number
(b) is not a multiple of 3
(ii) Find the number of paving stone between the houses.
(ii) How many paving stones does Kate not land on during the game?