Saturday, September 18, 2010

Today's problems are adapted from the NTSE series of books by Tata McGraw Hill for Class 8th (2008).  

1. How many non-overlapping discs of radius 1cms and fit in a disc of radius 2, 4, and 8cms?
2. 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.  
3. 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?
4. 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?
5. If Ms. Rich's income is 25% more than Mr. Poor, then by what percentage is Mr. Poor's income less than Ms. Rich?
6. 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?
7. 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?
8. 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.  
9. 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?
10. 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?