Batch 3 - Class 130 - Mathematical Hockey
Pre-Class Problem:
- (CombProbs Problem 52) Can you arrange numbers 1..9 in a circle so that sum of two neighbors is never divisible by 3, 5 or 7
- Answer: 5,6,2,9,4,7,1,3,8,(5) - One way to do this is to figure out all combinations which are "allowed", i.e. not divisible by 3,5,7. Then start to work with constraints like number 2 can only go with 6 and 9, and build from there. Number 4 can only go with 9 and 7, so that extends the sequence to 6,2,9,4,7, and so on.
Attendance: Smiti, Aneyaa, Khushi, Arnav, Anishka, Anshi, Liza, Palak, Diya, Damini
Class Notes:
Explain the rules of Mathematical Hockey
- Two teams; each player must take turns - can do random or assigned play as long as everyone gets turn
- 5 minutes per problem. Person to answer first wins if answer is right. Else the other person wins without having to answer
- If no one answers for 5 minutes, then 30 seconds for the next person scheduled on the team to answer
- Draw the hockey rink and goal posts and zones
- Display problems on TV screen
- Find a three digit prime formed by concatenation of consecutive digits (Answer: 109)
- Can you write 109 by inserting operators in 1_2_3_4_5_6_7_8_9
- Answer: 1*2+3*4+5*6+7*8+9
- Find the next in sequence 1+2=3; 4+5+6=7+8; 9+10+11+12 = 13+14+15
- Answer: 16+17+18+19+20 = 21+22+23+24
- Can you prove it? (http://teachersofindia.org/en/periodicals/right-angles-march-2014)
- On a digital clock, the display reads 6 ∶ 38. What will the clock display twenty-eight digit changes later?
- Answer: 7:02
- What is the remainder when 2015^2014 is divided by 2014?
- Answer: 1
- There is one coin with 50:50 probability of Heads:Tails. Amongst two people, you want to give first person twice as much chance of a win compared to the second person. How can you achieve it? (Tough)
- Answer: First person starts and they alternate in tossing the coin, till the first person to get the heads wins.
- Everytime I have to climb a flight of n stairs, I can take one stair step or leap 2 stairs on each step. In how many ways can I climb 4 stairs?
- Answer: Fibonacci(4) = 5.
- If no one gets the Fibonacci logic, ask for 6 stairs, and so on.
- You have 20 bags. What is the minimum number of eggs needed so that you have a different number of eggs in each bag?
- Answer: 19. Keep one bag empty and put one egg in each of the other 19 bags. Now put the empty bag in the next bag in the next bag in the next bag and so on.
- Logo Quiz
Homework Problem
- Solve for (TWO)^2 = THREE
- 138 ^ 2 = 19044 (tough)
References: