In a league of 5 football teams which play in a round robin
tournament show that it is possible for all five teams to be league
Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do this?
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
Based on the information in the first two tables most people agreed that Alison should live in B because it apparently has the highest population density and Charlie should live in E because it apparently has the lowest population density:
Population Density (based on total land area):
A = 142 people per sq km
B = 1101 people per sq km
C = 8 people per sq km
D = 202 people per sq km
E = 3 people per sq km
F = 390 people per sq km
G = 14 people per sq km
H = 54 people per sq km
(All results were rounded up to a whole number)
However, there was some confusion as to how to use the rest of the data:
Some suggested that Charlie should go and live in uninhabitable land! Are some of you wanting to get rid of Charlie? Alison perhaps...
Some didn't take into account that the population density would change after removing the uninhabitable land from the total land - Charlie and Alison would only be interested in the population density of the habitable land.
Some suggested suitable countries for Alison and Charlie, but didn't make it clear what calculations they had carried out to reach their conclusions.
The clearest analysis we received was from Komal, from India, who presented his results in this spreadsheet.
However, he assumed that Charlie would choose to live in an urban area. This didn't seem to take into account that Charlie "would like to get away from it all" - he'd be more likely to make his decision based on the population density of the non-urban areas.
Perhaps someone would like to work out the population density in the rural areas of each country.
Chris and Reiss from Wilsons' School suggested other information they might want to take into account before moving: