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Puzzle 1
My local library decided to hand out some of its old books to the 1,400 people who lived in the town.
To each library member, they offered 6 books, and to each non-member, they offered 4 books.
If only half of the members, and three-quarters of the non-members, accepted the books, how many books were given away?
Hint
As we don't know how of the people were library members, you can try a random number and see what happens.
Answer
4,200 books.
Reasoning
It doesn't matter how many library members there were, as 1/2 of them accepted the books, and each accepted 6 books, which is 3 books per member on average.
Similarly, it doesn't matter how many non-members there were as 3/4 of them accepted the books, and each accepted 4 books, which is again 3 books per non-member on average.
Double-Checking
Both the members and non-members accepted, on average, 3 books each.
And 1400 x 3 = 4200.
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Puzzle 2
Here is a curious grid! The sums of the shapes are shown at the end of each row, and at the bottom of each column.
What is the missing sum, and what is each shape worth?
Hint
How many miles were left at the start of yesterday?
Answer
336 miles.
Reasoning
To work these numbers out, it is perhaps easier to start at the end and work backwards.
Yesterday I travelled 1/3 of the distance to leave 21 miles, therefore there were 31.5 miles (=21 ÷ 2/3) at the start of yesterday.
On day 3 I travelled 3/4 of the distance to leave 31.5 miles, therefore there were 126 miles (=31.5 ÷ 1/4) at the start of day 3.
On day 2 I travelled 1/2 of the distance to leave 126 miles, therefore there were 252 miles (=126 ÷ 1/2) at the start of day 2.
On the first day, I travelled 1/4 of the distance to leave 252 miles, therefore there were 336 miles (=252 ÷ 3/4) at the start of the first day.
Double-Checking
On the first day, I travelled one quarter of the distance (84, leaving 252).
On day two, I travelled one half of the remaining distance (126, leaving 126).
On day three, I travelled three quarters of the remaining distance (94.5, leaving 31.5).
Yesterday I travelled one third of the remaining distance (10.5).
I now have 21 miles left to travel.
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Puzzle 4
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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It is now three years since I first asked for support, and I would like to sincerely thank everyone who has helped me. BrainBashers doesn't show adverts, and I continue to depend on the ongoing support from everyone who enjoys the site.
