May 2, 2010

1. Four Children A, B, C, and D are natives of four different countries (France, UK, USA, Argentina). Figure out the their native land from the following: (a) B is not from Americas (b) A is not born in Europe (c) D's native language is not English (d) C is not from the Northen Hemisphere.
2. Any natural number can be expressed as sum of at most four squares. For example: 13=1^2 + 2^2 + 2^2 + 2^2; 31=1^2+1^2+2^2+5^2; 39=1^2+2^2+3^2+5^2. Check this for 50; 91. (Learn More: Lagrange's four square theorem.)
   
3. You have only two measuring devices: a 5 liter bucket and a 3 liter bucket. Devise a scheme so that exactly 4 liter of water can be placed in in the 5 liter bucket. You can assume that you have a tap/pipe from which you can draw as much, and as often, water as you want.
4. Find the number if it satisfies the following: (a) If it is not a multiple of 4, then it is between 60 and 69. (b) If it is a multiple of 3, then it is between 50 and 59. (c) If it is not a multiple of 6, it is between 70 and 79.
5. You have in all 72 coins made up of nickels and dimes, totaling to $4.95. How many nickels you have?
6. A4 paper sheet is 8.5 inch by 11 inch. There are two ways to roll it - by long side and by short side - to form a cylinder. Which of these two cylinders will have larger volume?
7. Why are manhole covers made circular and not squares or rectangles or ellipses? (Think of their diameter versus the smallest side.)
8. Spread your fingers (and hand) on a piece of paper, and trace the contour. Between two consecutive fingers, you can measure the angle between two adjacent fingers (say the middle and ring). What is it? Do you think that this angle will be vastly different between a boy and a girl or between an adult and a child?
9. In the Papanack Zoo, you see 30 eyes and 44 legs. How many 2-legged and 4-legged animals are there?