Batch 1 - Class 10 - Mathematical Auctions

Attendance      Muskaan, Smiti, Jasmine, Tara, Harish and Parul

Today was a game of competition between two teams. In the Blue corner, Smazz (Smiti, Jasmine, Parul) and in the Red corner, Mmtm (Tara, Muskaan, Harish). Its a game of mathematical auctions, where a problem is presented, and the two teams bid for rights to answer the problem. The winner of the bidding gets to answer the problem. The winning bid is seized 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.

1. In a circle, use seven straight lines to draw maximum numbers of triangles. The circle's curvature can not form part of a triangle
Smazz bids 3 for 8 triangles, but gets only 7
Mmtm bids 1 for 8 triangles, and gets it and WINs

2. 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.
Mmtm no bid, smazz bid 1, get it with 4821+468=5289
Mmtm no bid, smazz also does not bid in spite of having an answer - WINs (nice bidding strategy to not bid since they are anyway winning on last round)

3. Use digits 1-6 in that order, and any 4 basic operators to make the sequence of natural numbers
Smazz bids and gives solutions for 1 to 5
Mmtm bids and gives solutions for 6 to 7
No one bids in next round - Mmtm WINs

4. 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

5. Divide 7 pizzas amongst 8 people equally with least straight cuts
Smazz bids 1, Mmtm bids 2 and gives a solution for 28 cuts
Smazz bids 6 and gives a 16 cut solution
Mmtm bids 1 and gives a 12 cut solution, WINs
Umm - Alok has a 7 cut solution here!

6. Unlink 20 link chain at minimum points to enable payments of 1-20 links individually
Tough bidding on this one. Smazz bids 6 eventually and does a 4 cut solution, WINs

7. Bonus problem for 10 coins - the homework toggles, truth teller problem
No one gets the answer, though it seems that Mmtm were almost there!
Overall Winner: MMtm with 25 chips against 20 chips that Smazz had!


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