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Post by liz on Mar 17, 2010 8:17:31 GMT
117.
Is this a catch question? To get any of the others you must first get one 6, if you see what I mean, so I will agree with BC.
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Post by Kimmy on Mar 17, 2010 11:56:02 GMT
6 dice: the probability for one six with 6 dice is .665, 2 from 12 = .619, 3 from 18 = .597 etc. To explain: For one dice, the probability is simply the probability of not getting a six on any dice, subtracted from 1, so: 1 - ((5/6)^6) = 0.665 (3 dp) For two sixes, we subtract the probability of no sixes on 12 dice and the probability of exactly one six on 12 dice from 1. The probability of one six is (5/6)^11 (for 11 non-sixes) times (1/6) (for one six) times 12 (for the 12 different arrangements of 1 six and 11 non-sixes - we have to count all these because (5/6)^11*(1/6) is the probability that dice 1 is six and the other 11 are not six, but dice 2, or dice 3, or any of the others could be the one that is the six), so: 1 - (5/6)^12 - (5/6)^11*(1/6)*12 = 0.619 (3 dp) Similarly for three sixes: 1 - (5/6)^18 - (5/6)^17*(1/6)*18 - (5/6)^16*(1/6)^2*18*17/2 = 0.597 (3 dp). Etc.  |
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Post by Kimmy on Mar 17, 2010 11:58:24 GMT
Lets go down the park.  Puzzle 121 As the auditor for my local theme park, I noticed that on Saturday there were 4296 children and 2143 adults and the takings were £98,718. However, on Sunday, there were 5146 children and 2807 adults and the takings were £122,570. How much were the adults tickets and children's tickets? |
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Post by BC on Mar 17, 2010 19:05:42 GMT
For one dice, the probability is simply the probability of not getting a six on any dice, subtracted from 1, so: 1 - ((5/6)^6) = 0.665 (3 dp) "SIMPLY" ;D |
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Post by BC on Mar 18, 2010 0:38:18 GMT
Puzzle 121 As the auditor for my local theme park, I noticed that on Saturday there were 4296 children and 2143 adults and the takings were £98,718. However, on Sunday, there were 5146 children and 2807 adults and the takings were £122,570. How much were the adults tickets and children's tickets? You know what, I'm going to be nice and let someone else have a go at answering this one. Isn't that kind of me? BC  |
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Post by Kimmy on Mar 18, 2010 10:34:01 GMT
All too shy to post.  Adult's tickets were £18 and children's were £14. |
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Post by Kimmy on Mar 18, 2010 10:35:29 GMT
Right let me Dubbin my boots and get playing.  Puzzle 122 During the recent BrainBashers football competition, 5 schools were competing. Each school played each other once, with 2 points for a win, 1 point for a draw, 0 points if they lost. Here are the final points after all of the matches: Longton 6 Fenton 5 Blurton 4 Hulton 2 Fulton ==?== How many points did Fulton end the season with? |
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Post by BC on Mar 18, 2010 22:28:49 GMT
Right let me Dubbin my boots and get playing. Puzzle 122 During the recent BrainBashers football competition, 5 schools were competing. Each school played each other once, with 2 points for a win, 1 point for a draw, 0 points if they lost. Here are the final points after all of the matches: Longton 6 Fenton 5 Blurton 4 Hulton 2 Fulton ==?== How many points did Fulton end the season with? A nice easy one to follow yesterday's "mission impossible".  5 teams all play 4 games each, with 2 points up for grabs per game. Let's say if every game is a draw, they would each get 4 points. So 4 games x 1 point x 5 teams = 20 points. In the table given, 17 points have been awarded, leaving 3 points available for Fulton. BC  |
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Post by BC on Mar 18, 2010 23:08:02 GMT
Unless the school had gone into administration, in which case 9 points would be deducted, leaving them on -6. Poor old Pompy.  Now we know why Harry jumped ship when he did! |
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Post by Kimmy on Mar 20, 2010 10:52:31 GMT
3: there were 5 teams therefore a total of 10 games took place. Hence Fulton's points must take the total to 20.  |
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Post by Kimmy on Mar 20, 2010 10:53:42 GMT
Looks like my numbers up.  Puzzle 123 Consider all of the numbers from 100 to 999. There are exactly four numbers where the sum of the digits cubed equals the original number. For example 153 = 1x1x1 + 5x5x5 + 3x3x3 = 1 + 125 + 27. Another two of the numbers are 370 and 407. What is the 4th? |
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Post by BC on Mar 20, 2010 23:27:08 GMT
Sorry - don't understand the question.  |
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Post by Kimmy on Mar 21, 2010 10:21:36 GMT
Nor me. But then again I don't understand any of them. 371: this can quickly been seen if you consider the fact that 370 is of this form and adding 1 to the number adds 1x1x1 to the sum. |
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Post by Kimmy on Mar 21, 2010 10:22:31 GMT
Fares please.  Puzzle 125 My local bus company has recently expanded and no longer has enough room for all of its buses. Twelve of their buses have to be stored outside. If they decide to increase their garage space by 40%, this will give them enough room for all of their current buses, plus enough room to store another twelve in the future. How many buses does the company currently own? |
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Post by BC on Mar 21, 2010 23:21:56 GMT
Fares please. Puzzle 125 My local bus company has recently expanded and no longer has enough room for all of its buses. Twelve of their buses have to be stored outside. If they decide to increase their garage space by 40%, this will give them enough room for all of their current buses, plus enough room to store another twelve in the future. How many buses does the company currently own? 12 outside plus 12 future = 24. 24 is 40% of current space. So 100% of current space is 60. (i.e. 60 x 40% = 24) So they have 60 currently stored, plus 12 outside = 72BC |
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Post by liz on Mar 22, 2010 8:14:37 GMT
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Post by Kimmy on Mar 22, 2010 11:33:00 GMT
72 buses: they have enough room for 60 of these, expanding the 60 capacity by 40% will give them enough room for 84 - which we know is 12 more than their current count.  |
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Post by Kimmy on Mar 22, 2010 11:37:11 GMT
There are some very shy people out there. Come on post your answer we are a friendly lot.  ;D Taken the same bus for a ride in the country.  Puzzle 126 If a farmer buys chicken feed for 57c per tonne, pig feed for $1.52 per tonne and cattle feed for 43c per tonne. How much of each would he have if he had 100 tonnes for $100? |
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Post by Kimmy on Mar 23, 2010 9:49:43 GMT
49 tonnes of chicken feed, 46 tonnes of pig feed and 5 tonnes of cattle feed.
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Post by Kimmy on Mar 23, 2010 9:51:20 GMT
OK all you people who wont join in YOUR NUMBERS UP.  Puzzle 127 What number comes next in this sequence? 986888 724864 143224 |
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Post by BC on Mar 23, 2010 23:17:28 GMT
OK all you people who wont join in YOUR NUMBERS UP. Puzzle 127 What number comes next in this sequence? 986888 724864 143224 No time to do yesterday's one, and can't do today's. Stumped. |
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Post by Kimmy on Mar 24, 2010 23:05:25 GMT
468: each line is generated by multiplying two digits at a time of the previous line. 986888 = (9x8)(6x8)(8x8) = 724864 = (7x2)(4x8)(6x4) = 143224 = (1x4)(3x2)(2x4) = 468.
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Post by Kimmy on Mar 24, 2010 23:07:08 GMT
Whats for dinner?  Puzzle 128 Mary needed 400ml of vegetable stock for a recipe she was following. However the only measuring containers she had were 300ml and 500ml. How can she measure out exactly 400ml? |
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Post by BC on Mar 25, 2010 22:42:57 GMT
1. Fill the 300 2. Pour the 300 into the 500 3. Fill the 300 4. Fill the 500 to the top from the 300 leaving 100 5. Empty the 100 into the caserole 6. Fill the 300 from the 500 leaving 200 in the 500 7. Empty the 300 into the caserole. There is now 400 in the caserole. But what to do with the 200 that's left in the  Give it someone who's bound to appreciate it. BC |
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Post by liz on Mar 26, 2010 8:09:50 GMT
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Post by Kimmy on Mar 26, 2010 17:15:30 GMT
She should fill the 500 ml container first and use this to fill the 300ml container, thereby leaving 200 ml in the larger jug. Then she could empty the 300ml container back into the stock jar and pour the 200ml from the larger container into the 300ml container. If she once again fills the larger container from the jar and again, fills the smaller container from this, the smaller container needs 100ml to fill it, which will leave 400ml in the larger container. |
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Post by Kimmy on Mar 26, 2010 17:16:06 GMT
Puzzle 129 Can you find three consecutive even numbers that total 85008 when multiplied together? |
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Post by BC on Mar 26, 2010 23:10:14 GMT
Puzzle 129 Can you find three consecutive even numbers that total 85008 when multiplied together? A nice easy one tonight... 42 x 44 x 46 BC |
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Post by Kimmy on Mar 27, 2010 11:25:06 GMT
Not for me. 42, 44 and 46. |
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Post by Kimmy on Mar 27, 2010 11:26:34 GMT
Back to school.  Puzzle 131 At the local BrainBashers Sunday School meeting, the teacher brought in some puppies. There were 20 more children than puppies. In the corner of the room, within the ant's nest, there were exactly 10 times more ants than children. In total, including the teacher, the children, the puppies and the ants, there were 1440 legs in the room. How many children attended? |
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