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 Mathematical Puzzles 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? [Ref: ZNXG] © Kevin Stone Direct Link: www.brainbashers.com?ZNXG Hint: It didn't matter how many library members or non-members there were. Answer: 4,200 books. 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. So both the members and non-members accepted, on average, 3 books each. And 1400 * 3 = 4200. Puzzle 2 Here is a curious grid, the sums of the shapes are shown at the end the row and at the base of each column. What is the missing sum? What are the different shapes worth? [Ref: ZJFC] © Kevin Stone Direct Link: www.brainbashers.com?ZJFC Hint: The square is worth 7. Answer: 31.Square   = 7 Triangle = 9 Circle   = 12 Arrow    = 3 Puzzle 3 Last week, I travelled from Birmingham to Glasgow (via bicycle). On the first day I travelled one quarter of the distance. On day two, I travelled one half of the remaining distance. On day three, I travelled three quarters of the remaining distance. Yesterday I travelled one third of the remaining distance. I now have 21 miles left to travel. How far is it from Birmingham to Glasgow in total? [Ref: ZZVA] © Kevin Stone Direct Link: www.brainbashers.com?ZZVA Hint: How many miles were left at the start of yesterday? Answer: 336 miles. 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. To work these numbers out, it is easiest 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 x 3÷2) 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 x 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 x 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 x 4÷3) at the start of the first day. Puzzle 4 Last week I travelled from London to Leeds, which is a distance of 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 round trip? The answer is not 50 mph. [Ref: ZTAH] © Kevin Stone Direct Link: www.brainbashers.com?ZTAH Hint: Remember that Time = Distance ÷ Speed, and Speed = Distance ÷ Time. Answer: 48 miles per hour.    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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