All entries for June 2009
June 22, 2009
What is the largest perfect square number that uses each digit 123456789 exactly once?
June 15, 2009
The M25 motorway completely encircles London, and in Britain we drive on the left. So if you travel clockwise around the M25 you stay on the outside carriageway, whereas travelling anti-clockwise keeps you on the inside carriageway, which is shorter. But how much shorter?
The total length of the M25 is 188km (117 miles), so the advantage of being on the inside carriageway outght to be quite a lot – shouldn’t it?
Suppose that two cars travel around the M25, staying in the outside lane – one going clockwise and one going anti-clockwise. Also suppose that the distance between these two lanes is always 10 metres (to make it specific).
How much further does the clockwise van travel than the anti-clockwise one? You should also assume that the roads all lie in a flat plane.
June 08, 2009
'It was a wonderful party,' said Lucilla to her friend Harriet.
'Who was there?'
'Well - there was one grandfather, one grandmother, two fathers, two mothers, four children, three grandchildren, one brother, two sisters, two sons, two daughters, one father-in-law, one mother-in-law and one daughter-in-law.'
'Wow! Twenty-three people!'
'No, it was less than that. A lot less.'
What is the smallest size of party that is consistent with Lucilla's description?
June 01, 2009
I drop a rock down a well, and it takes 6s to reach the bottom. If gravity is 10m/s², how deep is the well?