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 Mathematical Puzzles Puzzle 37 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 38 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 39 What is the sum of... ...all of the numbers from 1 to 1000? [Ref: ZONR] Direct Link: www.brainbashers.com?ZONR Hint: Add the first number to the last - does this help? Answer: 500,500. It's easiest to see that the first and last number are 1 and 1000, which add to 1001. The next two numbers we can add are 2 and 999, which add to 1001. The next two numbers to add are 3 and 998, which add to 1001. We can keep doing this 500 times, and in each case they add to 1001. And 500 x 1001 = 500,500. Puzzle 40 Which of these is correct: Six and six IS eleven or six and six ARE eleven? [Ref: ZYTW] Direct Link: www.brainbashers.com?ZYTW Hint: Is this a test of your English? Answer: Neither! The answer is twelve!

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