“Flip for $1 billion”: There’s one chance in 524,288 (2 to the power of 19) that you will wiin and 524,287 divided by 524,288 that you will lose $100. Even though the chance of losing is so high (“almost certain” in statistical language), when youo do win your winnings will more than make up for your losses. In fact, the average payout when playing this game is about $1800 per bet. “Flipping heck!”
George Nobl Problem:
Professor Nobl explained that the correct answer is one hour and 12 minutes. Here is how he solved it, he said. Fred paints a third of a room in one hour, and Mary a half. So together they can paint five-sixths of a room in an hour. To paint the entire room, they will need six-fifths of an hour, or an hour and 12 minutes.
Missing Numbers: ‘five-star’; ‘85000sq m floor area, $703m project with 1327 new underground carparks’; ‘33000 new international visitors,’ $90 million of ….. and 800 jobs. The 300-room, 5-star hotel will … further 150 jobs’; 3000 people or 4000 people for one-off events’.
Number of spare car-parking spaces. How about 8, or 9 with a tiny part of one on the lower right.
What is x? Try substituting 1,2,3,4. I think you have it solved now!
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The pink triangle is one third of the area of the square. Use half base x height formula for area of the triangle, etc.
The coffee cup logic puzzle – Answer is Cup 5 as all the others have blocked pipes. 🙂
6×6 for the maximum dog pen area of 36 sq meters.
Oxford Exam Answer: According to Rebecca Cotton-Barratt, of Christ Church, this maths question tests abstract thinking”
“I’d initially ask the candidate what shape they think will be formed, and then ask them how they can test this hypothesis,” Cotton-Barratt says.
“They might initially try sketching the ladder at different stages – but ultimately what we want is something that we can generalise and that is accurate (you can’t be sure that your drawing is that accurate, particularly when you’re making a sketch on a whiteboard and don’t have a ruler). So eventually they will fall back on maths, and try to model the situation using equations.
“If they get stuck we would ask them what shape the ladder makes with the wall and floor, and they’ll eventually spot that at each stage the ladder is forming a right-angled triangle. Some might then immediately leap to Pythagoras’ Theorem and use that to find the answer (which is that it forms a quarter circle centred on the point where the floor meets the wall).Of course, Pythagoras could easily find the hypotenuse – it is the green line along the water! (Hint: the hypotenuse is always opposite the right angle!)
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Frustratingly there is no definitive answer to the riddle, leaving guessers with no choice but to continue scratching their heads.
Dr Kevin Bowman, course leader for Mathematics at the University of Central Lancashire said: ‘You can interpret it in many ways; one way is no more correct than another.
“There’s no ambiguity in the first equation; 3 apples is 30, so one apple is worth 10.
The Fruit Puzzle…
This isn’t the first mind-bending puzzle to sweep the internet in recent months. Earlier this year, National Geographic’s puzzle asking you to identify which direction a bus is travelling in left thousands of adults scratching their heads (see earlier post). One person suggests that, “because all the bananas aren’t the same, you could say that they all represent different amounts. You might even say that the two coconut pieces in the third equation are different sizes, and therefore add up to three quarters or even seven eighths when put together. In that sense, there are an infinite amount of possible answers.”
Dr Kevin Bowman, course leader for Mathematics at the University of Central Lancashire said: ‘You can interpret it in many ways; one way is no more correct than another.
“There’s no ambiguity in the first equation; 3 apples is 30, so one apple is worth 10.”
Another said, “1 apple equals 10, coconut equals 6 and banana bunch equals 4 so your answer is 20.”
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All exterior angles of one coin add up to 360 degrees. Since a coin has 12 sides, each exterior angle = 30 degrees. Two angles are formed between the two coins. Therefore, the angle formed is 60 degrees.
Quite an easy pattern in the Oct 10-11 Post. Subtract the first two numbers to get the first number in the right column; add the first two numbers in the left column to get the last two of the right column!
Parking Lot Puzzle: Turn your computer screen upside down (or stand on your head), then it becomes easy 🙂
In each row, adding gives the last 2 digits and subtracting gives the first.
The blue cherry picker has an extension arm that can’t be seen very well. This has placed the workers closer to the camera and created a strong false sense of scale simply because your eye assumes that the workers should be on the same plane as the base of the cherry picker!
Yes, it was Major General Stanley in the “Pirates of Penzance!” Check out the link in the picture.
The extra rope needed is exactly 2 x pi or 6.28m!
Christmas Teaser: Today is the 1st of January. Bill’s 8th birthday was yesterday, so the day before (December 30) he was still 7 years old. This December he will turn 9 and, next year, will be 10!
What did the math mother feed her new baby? Formula Milk!
What is a bubble? It is a thin sphere of liquid enclosing air (in most cases) or another gas.
Number of toes = 5170
How many Mathematicians to change a light bulb? Why, n+1 of course (one to hold the light)!
Jan 24, 2014: Assuming a free fall rate of 9.8m/sec/sec it would take just 4.06sec to fall 81m.
= 1 (see first line in the post)
Yes, the TV show with hints of Mathematics and Physics (along with the usual tensions of flatmates?) – did you choose 79?
Leonhard Euler (1707-1783) was an incredibly productive mathematician who published almost 900 books! He took an interest in Latin Squares – grids where each row and column each contains a member of a set of numbers. This forms the basis for Sudoku!
Trig Ratios post: yes, the Sine and Cosine ratios are the same when their angles add up to 90 degrees! This relationship can be expressed as: Sine A = Cosine (90-A) or Cosine A = Sine (90-A)
Good work in identifying this trig pattern. Now, here is a follow up questions which we will address in the next post. Does this pattern suggest that there is a link between Sine and Cosine ratios? Come on, come on… be quick with your answer…Yes, well done – of course there must be!!
Yes, zero is an Integer (which keeps to negative and positive integers apart).
Sam had to position himself to make sure that he 8 the chocolate!
There are 7 days in a week (i.e. Modulo 7). 490 days will be the same day that you chose, so the 491st day will be tomorrow!
Yes, C is the missing section – giving the same difference between numbers in the rows and columns.
Other answers:
That’s a mean looking crocodile! Unless, of course, you knew that it measured just 40cm – yes, just over a foot long!! The camera’s wide angle lens has distorted the image and this makes tiny croc look menacing!
Yes, the 100m time for Bolt works out to be 37kms/hr or 22mls/hr. Of course that is just the average time, not the max speed he reached!
Category 3 climbs last approximately 5 kilometres (3.1 miles), have an average grade of 5 percent, and ascend 150 metres (500 feet).
Category 2 climbs are the same length or longer at an 8 percent grade and ascend 500 metres (1,600 feet).
Category 1 climbs last 20 kilometres (12.4 miles) with an average 6 percent grade and ascend 1,500 metres (4,900 feet).
Category H climbs are the hardest including an altitude difference of at least 1,000 metres (3,280 feet) from start to finish and have an average grade of at least 7 percent.
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Finding missing numbers is great fun and many readers are regular users of Sudoku. In the recent post (July 13) we find that the sum of the numbers in each row and column is 6, 12, ? Therefore, we need to get 18 as the sum in the final row and column. So, 9 is the missing number in order to complete the puzzle.
Great to see some recent posts on Calculus and we hope that some of our junior students (Years 6+) have a close look at these and develop an interest in this (more advanced) Mathematics.
Trend lines are a practical way to analyse the patterns of data over time and are particularly helpful in population, commerce and environmental change, such as the arctic ice post. The best way to find the answer to the question posed in this post is to click on the original article, copy the graph and paste into (e.g.) Word, using the landscape format. Then, using a ruler, carefully draw the same lines that I have shown in the post. This will help arrive at a more accurate answer. When you have the answer, post a comment to the blog and we can check it out to see if you are right (or close). Good luck Junior Mathematician!
1 year = 31 556 926 seconds
1729 – A rather dull number?
The mathematician G. H. Hardy was visiting the Indian mathematician Ramanujan while he was ill in hospital. Hardy was making small talk and remarked that 1729, the number of the taxi that brought him to the hospital, was a rather dull number. “No Hardy!” repled Ramanujan, “It is a very interesting number. It is the smallest number which can be expressed as the sum of two cubes in two different ways!” You see, even “dull” numbers have special properties!
By definition, a Paradox is an absurd statement which may prove to be true. The amazingly impossible designs of the artist Escher are excellent examples and his work is shown in the sculpture above. Mathematics is one large system of logic – a kind of universal language that transcends individual civilizations and specific languages. As such, certain paradoxes have arisen that have troubled mathematicians from ancient times to the present. Some are false paradoxes in that they do not present actual contradictions, but are merely slick logic tricks. Others have shaken the very foundations of Mathematics – requiring brilliant, creative mathematical thinking to resolve. Others remain unresolved to this day. Check some of these out in the Math Forum.
