Batch 3 - Class 213 - Mathematical Hockey

• A monk climbs a mountain. He starts at 8AM and reaches the summit at noon. He spends the night on the summit. The next morning, he leaves the summit at 8AM and descends by the same route that he used the day before, reaching the bottom at noon. Prove that there is a time between 8AM and noon at which the monk was at exactly the same spot on the mountain on both days.
• Answer: Let the monk climb up whichever way he wants. At the instant he begins his descent the next morning, have another monk hike up traveling exactly as the first monk did the first day. At some point, the two monks will meet on the trail. That is the time and place we want!

• Two teams; each player must take turns - can do random or assigned play as long as everyone gets turn
•  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 screenx`x`

• A building has 10 floors. One person lives on the ground floor, two on the second floor, three on the third, and so on. On which floor does the elevator stop most frequently? 
• Ground - everyone has to go through the ground floor
• Emma would like to buy 9 chocolate bars, but she is $2 short. If she buys 5 chocolate bars, she will have $4 left over. What is the price of a single chocolate bar? 
• $ 1.5
• Two sheets of paper of the same size are lying on a table, so that one partially covers the other as shown in the figure. For the bottom page, which has greater area, the covered part or the uncovered part? 

• Answer: Uncovered
• In the proud country of Nosuchplacia every 20th mathematician is a musician, while every 30th musician is also a mathematician. Are there more mathematicians or musicians in Nosuchplacia? How many times more? 
• Answer: 1.5x musicians over mathematicians
• In Nosuchplacia, if you want to drive from BigCity to BiggestCity you have to pass through 20 tolls. In the first one you have to pay 3 dollariums, the next one requires 7 dollariums, the next one 11 dollariums, and so forth; each toll having you pay 4 dollariums more than the previous one. How much money does the trip cost? 
• Answer: 3x20+4x(19.20/2) = 820
• (Hard - Double Points)  On a 8 × 8 grid, can one place beans, no more than one bean per square, so that every column contains the same number of beans, but no two rows have the same number of beans?
• Answer

• A man wanted to get into his work building, but he had forgotten his code. However, he did remember five clues. These are what those clues were:
1. The fifth number plus the third number equals fourteen.
2. The fourth number is one more than the second number.
3. The first number is one less than twice the second number.
4. The second number plus the third number equals ten.
5. The sum of all five numbers is 30.

• Answer: 74658
• a..i are numbers 1..9 (no repetitions). What is the value of "h"?

• Answer: 7 or 1
• (Brainteaser - Hard) Whats next in the sequence? 1 11 21 1211 111221 
• Answer: 312211
• (Auctions Exercise) How many triangles can you find?

• Answer: 35
• (Auctions Exercise) How many non-congruent triangles can be drawn on a 3x3 grid of dots?
• Answer: Eight (first take everything with base 1, and then with base 2, and then with diagonal base)

• Minesweeper - The number in following cells indicates the number of mines in cells neighboring the numbered cell. A numbered cell doesnt have a mine. Find the total number of mines

• Answer: 11
• What is the four-digit number in which the first digit is one-third the second, the third is the sum of the first and second, and the last is three times the second? 
• Answer: 1349
• Memory Game - Look at the picture below for a minute and memorize. We will then ask individual people to recollect some cells

• (Geoffrey - 143) Three dutchmen and their wives go shopping hogs, and each buys as many hogs as he or she pays for each hog. Each husband spends Rs 63 more than respective wife. Husbands are Hendrick, Elas and Cornelius. Wives are Gurtrun, Katrun and Anna. Hendrick buys 23 more hogs than Katrun, while Elas buys 11 more than Gurtrun. What are the names of each man's wife?
• Answer: Pairs are 32/31, 12/9, and 8/1 - we can now see integers that differ by 23 and 11. So its Hendrick-Anna, Elas-Katrun and Cornelius-Gurtrun