Batch 2 - Class 08 - General problems, Light (2)

• Count number of trailing zeros in 320! http://www.artofproblemsolving.com/Videos/external.php?video_id=80 

  Answer: 78 (The key insight is that every 5 as a factor yields a trailing zero in the factorial product (when added to an even number, of which there are enough available in the factorial product). Thus there are 320/5=64 multiples of 5. The multiples of 25 give two zeros, and hence need to be added - there are 320/25=12 of these. The multiples of 125 give 3 zeros, and hence need to add those - there are two of those. Total 64+12+2=78)
• MartinShCol - 1.14 - There are bowling pins of red color and black color. Can you select 10 pins from these and place them in position of bowling pins, so that no equilateral triangle has all vertices of the same color?

  Answer: This is not possible. Progressively placing the pins starting from the center position helps arrive at the conclusion.

• MCDiaries - Pg 127, Warmup 2 - Anisha and Muskaan want to buy an ice-cream. Muskaan is Rs 3 short, and Anisha is Rs 15 short. They decide to pool their money together and buy the ice-cream. They are still Rs 3 short. How much does the ice-cream cost?

  Answer: Rs 15. The fact that they are together short by Rs 3 (same as how much Muskaan is individually short) means Anisha has no money. Since she is Rs 15 short, the ice-cream must cost Rs 15.

• Bending of light when it goes from one medium to another, angle of incidence and refraction

  Analogy through a car going from smooth surface to muddy one
• Coin becomes visible when you add water to a saucer
• Disappearing coin placed under a glass of water. Reappears if you put some water on the coin
• Broken pencil experiment
• Refractive index
• Disappearing prism when you fill the glass with oil
• Bending of laser light through a prism
• Bending of laser light through a glass slab
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• Homework Puzzle: How many non-attacking bishops can you place on a 101 x 101 chessboard?