Batch 2 - Class 09 - Mathematical Auctions

Attendance      

Today was a game of competition between the three teams. Its a game of mathematical auctions, where a problem is presented, and the teams bid for rights to answer the problem. The winner of the bidding gets to answer the problem. The winning bid amount is forfeited by the house. If they answer correctly, then a minute is given to all teams to think of a better answer, and the bidding resumes. The final bidding winner (after which no one is willing to bid) wins the round and the prize associated with each problem.

Value of each problem 10 coins. Minimum bid 1 coin. Initially give 40 coins to each team.

1. Using five times digit 1, represent as many consecutive natural numbres as possible, starting with 1. You can use arithmetic operators + - X / and parentheses.

Ninja Dolphins bid 4 coins and give answer for 1-6 - WIN

2. In a circle, use seven straight lines to draw maximum numbers of triangles. The circle's curvature can not form part of a triangle

Awesome bids 6 coins to draw 9 triangles, draws only 6

Awesome bids 7 coins and draws 8 triangles

Ninja Dolphins bids 3 coins and draws 9 triangles - 5 pointed star and then two lines dividing two triangles into 4 each - WIN

3. BOA + BACK = SCAM. Assign digits to letters so that the equation works. Different letters must stand for different digits. The bids can continue till the bidder can provide another unique answer beyond what have been provided earlier.

Ninja Dolphins bid 4 coins and give 368+3819=4187 - WIN

(another answer 4821+468=5289)

4. Use digits 1-6 in that order, and any 4 basic operators to make the sequence of natural numbers

Series of bids with Ninja Dolphins and Awesome giving one answer at a time

Awesome takes it a notch up with solutions upto 13

Ninja Dolphins wins with solutions to 15 

Awesome tries 16 and loses. Ninja Dolphins WIN

5. Divide 7 pizzas amongst 8 people equally with least straight cuts

Ninja Dolphins and Awesome know the answer. So zero value (7 cuts)

Homework: Unlink 20 link chain at minimum points to enable payments of 1-20 links individually

6. How many squares with vertices at the marked points can you draw?

Ninja Dolphins gets to 28 - WIN

Actual answer is 30

7. Preclass problem: How many non-attacking bishops can you place on a 101 x 101 chessboard?

Awesome bids 9 and gets 103

Blue bids 10 and gets 200 - WIN

Overall Winner: Awesome end with 15, Blue with 36, and Ninja Dolphins win with 61

Instructor Notes and References: MC Diaries Y1, Pg 213-217 for description and first three problems

                                                MC Diaries Y1, Chap 4 for next three problems

                                                Unused problem: MC Diaries Y1, Chap 6. Problem Set Problem 2 (Note that there are 30 answers, so a smaller problem might be better)

                                   Mathematical Circle Diaries, Year 1, by Anna Burago

NOT USED 5. Use 5 2's and any 4 basic operators to make the sequence of natural numbers

Mmtm bids 0, smazz bids 1 and gives solutions till 3

Mmtm bids 3 and gives solutions till 4

Smazz bids 3 and gives solutions till 10 and WINs