- 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

### 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

### September 6. 2010 (Labour Day)

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?

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