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Post by Kimmy on Dec 19, 2009 10:48:05 GMT
Puzzle 16 The BrainBashers football world tour is well underway and Alfred is planning the journey to each country. Unfortunately, the BrainBashers atlas software is playing up again and has worked out the mileage incorrectly, as shown below. China 3,500 Finland 6,000 Chile 3,700 Jamaica 3,800 Wales 6,000 According to the software, how many miles is it to Germany? Being a duffer I wouldn't know where to start on these questions.  |
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Post by BC on Dec 20, 2009 13:19:47 GMT
Germany is 8,300 miles A = 100, B = 200, C = 300, etc.  |
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Post by BC on Dec 20, 2009 13:21:01 GMT
Sorry about the That was meant to be a smiley face.  |
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Post by Kimmy on Dec 21, 2009 11:35:26 GMT
8,300: each letter of the country is worth 100 miles based on its position in the alphabet. Therefore, Germany = 7 + 5 + 18 + 13 + 1 + 14 + 25 = 83 * 100 miles.  |
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Post by Kimmy on Dec 21, 2009 11:36:33 GMT
Puzzle 17 Last week, I travelled from Birmingham to Kansas. 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 Kansas in total? |
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Post by BC on Dec 21, 2009 16:53:28 GMT
Take the journey as 100 points: Day 1 = 1/4 means I covered 25 points and have 75 points left Day 2 = 1/2 of remainder means I covered 37.5 points and have 37.5 points left Day 3 = 3/4 of remainder means I covered 28.125 points and have 9.375 points left Day 4 = 1/3 of remainder means I covered 3.125 points and have 6.25 points left If 6.25 points = 21 miles, then the ratio between them is 3.36 (i.e. 21/6.25) 3.36 x 100 points = 336 milesFingers crossed.  |
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Post by Kimmy on Dec 22, 2009 8:36:41 GMT
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. |
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Post by Kimmy on Dec 22, 2009 8:37:09 GMT
Puzzle 21
A plane maintains an average speed of 225mph from London to New York. It then returns from New York to London at an average speed of 180mph. What is the average speed for the entire journey?
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Post by BC on Dec 23, 2009 7:25:41 GMT
This has got to be a trick question. Unfortunately, I can't spot the trick. Can it be as simple as (225 + 180) / 2 = 202.5 ? Do we need to take into account wind speeds? Exact routes and resultant differring mileages? Circling above Heathrow whilst they confirm a runway? Go on then... what's the trick? |
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Post by Kimmy on Dec 23, 2009 9:31:31 GMT
200mph: if the one-way distance was 1000 miles (for example), the outward journey took 1000/225 hours and the return journey took 1000/180 hours. Therefore the total time taken was (1000/225 + 1000/180) hours for 2000 miles. So the average speed was 2000 / (1000/225 + 1000/180) which equals 200mph. The answer remains the same if you change the distance to any number of miles.
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Post by Kimmy on Dec 23, 2009 9:32:06 GMT
Puzzle 22 You have the misfortune to own an unreliable clock. This one loses exactly 24 minutes every hour. It is now showing 3:00am and you know that is was correct at midnight, when you set it. The clock stopped 1 hour ago, what is the correct time now?  |
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Post by BC on Dec 24, 2009 12:14:15 GMT
At 1 am, the clock showed 00:36 At 2 am, the clock showed 01:12 At 3 am, the clock showed 01:48 At 4 am, the clock showed 02:24 At 5 am, the clock showed 03:00 So if the clock stopped an hour ago, it is now 6 am. |
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Post by Kimmy on Dec 25, 2009 10:16:13 GMT
6:00am: since the clock is losing 24 minutes every hour, for every real hour that has passed, the clock will only show 36 minutes. Since the clock shows 3:00am, we know that 180 clock minutes have passed. This therefore equals 300 real minutes and hence 5 hours. The clock stopped 1 hour ago and the time must now be 6.00am. |
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Post by Kimmy on Dec 25, 2009 17:37:07 GMT
Puzzle 1 As a gift for Christmas, a wealthy family gives its children seventeen computer games. The youngest child gets one ninth of the games, the middle child gets one third of the games and the oldest child gets one half of the games. How are the games divided up, remembering you cannot have part of a computer game? |
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Post by BC on Dec 25, 2009 19:18:52 GMT
Puzzle 1 As a gift for Christmas, a wealthy family gives its children seventeen computer games. The youngest child gets one ninth of the games, the middle child gets one third of the games and the oldest child gets one half of the games. How are the games divided up, remembering you cannot have part of a computer game? I have no idea! Wasn't it a different one ealier, or have I finally lost the plot? Hope you've had a good Christmas Day.  |
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Post by Kimmy on Dec 25, 2009 20:43:26 GMT
BC You are correct. I somehow deleted it but I have found it again. Yes had a nice day thank you and I hope you did. Puzzle 23 Daniel, my son, is exactly one fifth of my age. In 21 years time, I will be exactly twice his age. My wife is exactly seven times older than my daughter, Jessica. In 8 years time, my wife will be three times older then Jessica. How old are Daniel and Jessica now? |
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Post by BC on Dec 26, 2009 19:48:51 GMT
Husband and Son: H/5 = S and (H+21)/2 = S+21 works when H = 35 and S = 7 Wife and Daughter W/7 = D and (W+8)/3 = D+8 works when W = 28 and D = 4 So, Daniel is seven and Jessica is fourFingers still crossed. |
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Post by BC on Dec 26, 2009 19:55:11 GMT
Puzzle 1 As a gift for Christmas, a wealthy family gives its children seventeen computer games. The youngest child gets one ninth of the games, the middle child gets one third of the games and the oldest child gets one half of the games. How are the games divided up, remembering you cannot have part of a computer game? Coming back to this one, if there were 18 games, then: The youngest child gets one ninth = 2 the middle child gets one third = 6 the oldest child gets one half = 9 2+6+9 = 17 But there are 17 games. Perhaps two of the children are sharing one game. |
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Post by Kimmy on Dec 27, 2009 10:31:00 GMT
Husband and Son: H/5 = S and (H+21)/2 = S+21 works when H = 35 and S = 7 Wife and Daughter W/7 = D and (W+8)/3 = D+8 works when W = 28 and D = 4 So, Daniel is seven and Jessica is fourFingers still crossed. Daniel is 7 years old and Jessica is 4 years old. |
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Post by Kimmy on Dec 27, 2009 10:33:10 GMT
Puzzle 1 As a gift for Christmas, a wealthy family gives its children seventeen computer games. The youngest child gets one ninth of the games, the middle child gets one third of the games and the oldest child gets one half of the games. How are the games divided up, remembering you cannot have part of a computer game? Coming back to this one, if there were 18 games, then: The youngest child gets one ninth = 2 the middle child gets one third = 6 the oldest child gets one half = 9 2+6+9 = 17 But there are 17 games. Perhaps two of the children are sharing one game. The family are a little stuck until they borrow a game from their neighbours. This allows: one ninth of 18 is 2, one third of 18 is 6 and one half of 18 is 9. Now, this adds to 2 + 6 + 9 = 17, leaving the spare game to give back to their neighbour! |
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Post by Kimmy on Dec 27, 2009 10:34:13 GMT
Puzzle 24
After a day picking strawberries I had a basket full. I ate 5 and gave Geoff half of the remaining. I then ate another 3 and gave Simon one third of the remaining. I ate another 6 and then gave Kim two thirds of the remaining. I now had 34 strawberries left. How many did I start with?
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Post by BC on Dec 27, 2009 23:33:26 GMT
Puzzle 24 After a day picking strawberries I had a basket full. I ate 5 and gave Geoff half of the remaining. I then ate another 3 and gave Simon one third of the remaining. I ate another 6 and then gave Kim two thirds of the remaining. I now had 34 strawberries left. How many did I start with? Can I just say I am waiting several hours to give someone else a chance to have a go!  Anyway... With this one, I started trying to work out the equasions and got myself confused. So decided to work from the bottom up (so to speak): 34 is third, so there were another 68 given to Kim You ate 6 makes 108. 108 is two thirds, so you gave simon 54 You ate 3 makes 165 165 is half so you gave Geoff 165 You ate 5 makes 335Fingers in their usual crossed state! |
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Post by Kimmy on Dec 28, 2009 10:25:10 GMT
335 strawberries. I started with 335. Ate 5 leaving 330, giving 165 away (leaving me with 165). I then ate another 3 leaving 162, and gave away 54 (leaving 108). I ate 6 more leaving 102, and gave away 68. This left me with 34.  |
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Post by Kimmy on Dec 28, 2009 10:26:53 GMT
Puzzle 25 I am compiling the new BrainBashers world almanac and it now contains lots more pages. I know that it takes 333 digits to print the page numbers in sequence. How many numbered pages does the book have and how many times does the number 3 appear? (I think I will stick to finding winners.)  |
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Post by BC on Dec 28, 2009 16:13:31 GMT
Puzzle 25 I am compiling the new BrainBashers world almanac and it now contains lots more pages. I know that it takes 333 digits to print the page numbers in sequence. How many numbered pages does the book have and how many times does the number 3 appear? (I think I will stick to finding winners.) Numbers 1 - 10 are made up of 11 digits Numbers 11-100 are made up of 181 digits (89 x 2 digit numbers + one 3 digit) Sub total 11 + 181 = 192 digits (and carry forward 100 pages) ___ Now calculate how many pages over 100 are made up of the remaining digits: 333 - 192 = 141 three digit numbers 141/3 = 47 pages ___ 100 pages + 47 pages = 147 pagesHere's hoping. |
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Post by Kimmy on Dec 29, 2009 9:09:28 GMT
There are 147 pages and the number 3 appears 35 times.  |
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Post by Kimmy on Dec 29, 2009 9:12:51 GMT
Puzzle 26 Peter decided to walk to the local waterfall, 10 miles away. At the moment he started, his dog ran off from his side and proceeded to the waterfall at a constant 8 miles per hour. As soon as the dog reached the waterfall, it started the return journey to Peter, keeping to the same speed. The dog continued this odd behaviour until Peter reached the waterfall. If Peter kept to a constant 4 miles per hour, how far did the dog run in total?  |
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Post by BC on Dec 29, 2009 16:23:20 GMT
There are 147 pages and the number 3 appears 35 times. Oh. I missed the bit about the number three. Dog-nab-it. Looks like it's just the two of us on this thread KP.  |
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Post by BC on Dec 29, 2009 16:33:08 GMT
Puzzle 26 Peter decided to walk to the local waterfall, 10 miles away. At the moment he started, his dog ran off from his side and proceeded to the waterfall at a constant 8 miles per hour. As soon as the dog reached the waterfall, it started the return journey to Peter, keeping to the same speed. The dog continued this odd behaviour until Peter reached the waterfall. If Peter kept to a constant 4 miles per hour, how far did the dog run in total? Peter will take 2.5 hours to walk to the waterfall at 4pmh. It is probably irrelevant that the dog runs back and forth, but I have been known to be wrong! So at 8mph, the dog will have covered 20 miles in 2.5 hours. Here's hoping. |
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Post by Kimmy on Dec 30, 2009 11:43:10 GMT
20 miles: Peter took 2.5 hours to reach the waterfall. The dog was always running at 8 miles per hour, therefore it ran 20 miles.  |
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Anyway...
