- How many non-overlapping discs of radius 1cms and fit in a disc of radius 2, 4, and 8cms?
- Given a disc D of radius 2 cm lying on a table, whats the maximum number of discs of the same radius you can place (lying on the table) so that each of them is touching D and none of the discs overlap.
- These are classical packing problems: for example how many balls of radius 1cm can fit in a giant ball of radius 4cms? How can we estimate this number? How can we estimate the volume of the gaps?
- The train coming from Toronto to Ottawa, traveling at a speed of 60Km/Hr made me wait for 10 seconds at the signal. How long (in mts) is the train?
- If Ms. Rich's income is 25% more than Mr. Poor, then by what percentage is Mr. Poor's income less than Ms. Rich?
- A door-to-door salesman sells two cookie jars, each for $10.00 - one to Ms. Tough-Bargain and the other to Mr. What-ever. For Ms. Tough-Bargain he make a loss of 10% and for Mr. What-ever he makes a profit of 10%. Did the salesperson made an overall profit or loss?
- Anant's piggy bank has in all change for $33.00. It consists only of quarters, dimes and nickles, in the ratio of 5:3:2. How many coins of each type Anant has?
- We know that in an equilateral triangle, each interior angle is 60 degrees; in a square it is 90 degrees; what do you think it will be in a regular pentagon; regular hexagon; and how we will go about finding it.
- The Rideau River near my department has pretty fast current. Ottawa police does their rescue drill operations once in a while. They go down-stream, and then up-stream. In 10 minutes, the rescuers travel the downstream in their inflatable boats covering the distance of 1 km. Upstream, for the same distance, it takes them twice as long. What is the speed of the current?
- In the school's Terry Fox Run, I came 19th from the top and 235th from the bottom. How many kids participated in the run?
Saturday, September 18, 2010
Today's problems are adapted from the NTSE series of books by Tata McGraw Hill for Class 8th (2008).
Monday, September 6, 2010
We met last two weeks, and did problems from the book "Learning Maths 6B by Norrin Hasim (Singapore Asian Publications)". I highly recommend this book for middle school kids for a variety of very nice problems - I haven't seen other levels of this book - but 6B has lots of nice geometric problems. Today's Problems 1-3 are based on this.
- Find the area of the American Football in the square of side 45 cm long, in the above picture.
- 1/5th of Anant's mm's are same as that of 1/3rd of Aditya's. If Aditya gives Anant 24 mm's (unlikely though!), Anant will have thrice as many mm's as Aditya. How many they had to begin with?
- A solid iron ball of volume 576 cubic-centimeter is cast into nine identical solid cubes. What are the dimensions of the cube?
- What about the other way around? Suppose you have 16 identical cubes, each having a side length of 2cm long, is cast as a solid ball. What is its radius?
- A string forms an equilateral triangle, whose sides are 3.14cms long. The same string is now reshaped as a circular ring. What is the radius of the ring?
- A circular race track has a inner radius of 56m and outside radius of 63m. What is the total area of the track itself?
- In the above problem, if the 7mts wide track is divided into 7 equally spaced ones- 1mts each, 7 racers need to run the full length of the track once - how should you place them so that each of them cover the same length?
- The difference between the ages of Mr. Young and Ms. Old is 45 years and the ratio of their ages is 3:8. What are the ages of Mr. Young and Ms. Old.
- Divide 25 into two parts, such that 4 times of one part is the same as 6 times the second.
- In a large movie hall, seats are assigned with respect to row and column numbers. In all there are 1296 seats, and the number of rows are the same as columns - how many rows are there?