Reasoning
Take the numbers in pairs, square the first, and reverse the digits.
1 1 (1 x 1 = 1, reversed is 1)
2 4 (2 x 2 = 4, reversed is 4)
3 9 (3 x 3 = 9, reversed is 9)
4 61 (4 x 4 = 16, reversed is 61)
5 52 (5 x 5 = 25, reversed is 52)
6 63 (6 x 6 = 36, reversed is 63)
7 94 (7 x 7 = 49, reversed is 94)
so we require:
8 46 (8 x 8 = 64, reversed is 46)
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Puzzle 156
Last week I travelled from London to Leeds, a distance I measured as 174 miles.
I started at 9.15am and completed the journey with an average speed of 40 miles per hour.
On the way back, in the evening, I travelled exactly the same route, starting at 5.15pm. The traffic was light, and I completed the journey with an average speed of 60 miles per hour.
What was the overall average speed for the round trip?
Hint
Remember that Time = Distance ÷ Speed, and Speed = Distance ÷ Time.
Answer
48 miles per hour.
Reasoning
Using:
Time = Distance ÷ Speed
Speed = Distance ÷ Time
The outward journey took 174 miles ÷ 40 mph = 4.35 hours.
The return journey took 174 miles ÷ 60 mph = 2.9 hours.
So I travelled a total of 2 x 174 = 348 miles. I did this in a total of 4.35 + 2.9 = 7.25 hours.
My overall average speed was therefore 348 miles ÷ 7.25 hours = 48 miles per hour.
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