Batch 2 - Class 01 - Warmup Games

• (Trickiest Page 36) Move one nail to make 6 squares in following figure (7 answers: move any of the inside 7 nails to bottom gap)

• (MartinShCol - 4.17) How many times in 24 hours do the hour and minute hands overlap - Answer 22. Starting from 12 noon, the next overlap is at 1 hr and 5+ minutes, the second at 2 hr and 10+ minutes and so on. Thus, the overlap is not every 60 minutes, but about every 65 minutes. Hence in a 12 hour period, there are only 11 overlaps and not 12. Mathematically, in the duration that the hour hand covers x distance, the minute hand covers 12 x distance, and hence the difference is 11x. This difference is an integer number of revolutions since relative to hour hand the minute hand has moved integral number of revolutions more, i.e. 11x should be integral. There are 11 solutions to this (1/11, 2/11 and so on. Note that 0/ 11 and 11/11 correspond to 12 noon and hence are the same solution), each corresponding to one overlap.

  How many times would the hour, minute and second hands all overlap - Answer 2. Like above, hours and seconds overlap at integer values of 719x. Since 11 and 719 are both prime, there are only two values of x, i.e, 0 and 1 that satisfy both equations (both correspond to 12 noon and midnight respectively)Problem for parents: How many times do minutes and seconds hand overlap in 24 hours?

• (MC - 0 - 2) Ann, John, and Alex went to Disneyland with ticket costing $5 per head (yes, Indian kids wanted dollar pricing!). But they have only $10, $15, and $20 chips. How do they pay for the tickets.

  Answer: Ann pays $15 and buys three tickets. John and Alex give Ann $20 chips, and get $15 back each.Rejoinder: What if Ann has only $10 chips, John has only $15 chips, and Alex has only $20 chips.

• (Contributed by Manas) There are four people who need to cross a bridge. They take 10, 5, 2, and 1 minutes respectively to cross a bridge. There is only one light and anyone crossing the bridge must use it. Maximum of two people can cross the bridge at any time. What is the minimum time in which all four people can cross the bridge?

  Answer: 17. 2 and 1 cross, 1 comes back, 5 and 10 cross, 2 comes back, 1 and 2 cross

• Joke: Circle 6 numbers that total to 21 in the following grid (Answer: First three and last three inverted)

• http://www.mathteacherscircle.org/assets/session-materials/TShubinmathgames.pdf - 

  There are 25 matches on a table. During each turn, a player can take any number of matches between 1 and 4. The player that takes the last match wins. (Answer: 5,10,15,20)There are 25 matches in a pile. A player can take 1, 2, or 4 matches during each turn. The player who cannot continue (no more matches left) loses. (Answer: 3,6,9)Same game as above but it starts with 24 matches. (4,9,14,19,24)

• Answer: (1) The long and short of IT (2) Think outside the box (3) Last in, first out (4) Underwear (5) Above the line (6) I Understand

• (Moscow - 11) Wolf, Goat and Cabbage river crossing - A man has to take a wolf, goat and cabbage across the river. The boat has enough room for the man and one of the wolf/goat/cabbage. Wolf eats goat, Goat eats cabbage, unless the man is with them. How do they cross the river?
• Answer: Take Goat, Come back, Take cabbage, Bring Goat, Take Wolf, Come back, Take Goat

• (Moscow - 88) There are 11 kids in a circle. Count clockwise, incrementally 1, 2, 3, 4...10. At each counting, eliminate the person after that position and restart counting from next person onwards. The last survivor wins. Where would you start the counting so that you win? What if there are 9 kids? 
• Homework: Take A, 2, 3,...10, J, Q, K from a deck of cards. Arrange them in a pile, such that 1st top card is "1", then put the next top card at bottom, and second card should be "2", then put next 2 cards one by one at bottom and third card should be "3", and so on.