Math Club – January
Week 1
- The Knight ToursA proper knight’s tour is one in which the knight covers all the squares of the chessboard exac…1 answers
- DIY Challenge 1: A path across the 5x5 boardIn a 5×5 chessboard, find a path which starts at one corner and ends at any other corner. You c…6 answers
- DIY Challenge 2: Cover the most squaresWhat is the maximum squares you can cover in a 5×5 grid without intersecting any lines during t…7 answers
- DIY Challenge 3: Where a 7x7 tour can start and endBelow is a 7×7 chessboard. It is given that a knight’s tour is possible for this grid! Can you …7 answers
- DIY Challenge 4: A path on the 8x8 boardCan you find a possible path for the 8×8 chessboard? Do you see some interesting patterns as yo…6 answers
- DIY Challenge 5: Why the 4x4 board failsThe 4×4 chessboard! We tried finding a path for the Knight’s tour for a 4×4 grid. Is this possi…5 answers
Week 2
- Towers of HanoiSImulation Link:…
- DIY Challenge 1: Four disksSuppose you have 4 disks on peg A . You need to move them to peg C. How many moves will you nee…8 answers
- DIY Challenge 2: Writing out the steps for threeCan you write down all the steps involved in solving the problem for 3 disks ?…7 answers
- DIY Challenge 3: Four disks, built from threeYou have already solved the problem for 3 disks in the previous challenge. Can you write the st…5 answers
- DIY Challenge 4: From 9 disks to 10Imagine that you found a way for the solve the problem for 9 disks in 511 moves . How many move…6 answers
- DIY Challenge 5: A systematic way for eight disksHow would you go about solving the complete problem for 8 disks? Can you think of a systematic …5 answers
Week 3
- Plurality Voting1 answers
- Points Voting1 answers
- DIY Challenge 1: Plurality against pointsWhich dish will be the winner by the plurality voting system and the points voting system? Whic…10 answers
- DIY Challenge 2: Making the two systems disagreeCan you make choices which will lead to different winners with the 2 voting systems – Plurality…7 answers
- DIY Challenge 3: Design your own voting methodImagine that there are 4 options of food and 4 friends to choose the dish. If you had the power…4 answers
- DIY Challenge 4: Choosing the points for each rankThere are 4 foods now: Burger, Pasta, Salad and Chicken. You can choose the points for each ran…6 answers
Week 4
- Head to head voting1 answers
- DIY Challenge 1: Head-to-head comparisonsThere are 4 foods. Chicken, Burger, Pasta and Salad. How many comparisons will we need to make …9 answers
- DIY Challenge 2-aIn the previous challenge, many students responded that we need more items. Let’s say, you had …1 answers
- DIY Challenge 2: When plurality and head-to-head disagreeCan you create your own situation with choices that winners with plurality voting and head to h…10 answers
- DIY Challenge 3: All three methods disagreeCan you create your own situation with choices that winners with all three voting methods are d…7 answers
- DIY Challenge 4: All three methods disagree, with five votersCan you create your own situation with choices that winners with all three voting methods are d…3 answers
- DIY Challenge 5: Design the fairest electionYou are the election designer of your city. There are 3 candidates. Which voting mechanism, is …6 answers
Week 5
- RulesRemember: All squares should get covered…
- DIY Challenge 1: Can blue win?Is it possible to make the blue win in the following example? Can you show a way?…7 answers
- DIY Challenge 2: Why blue cannot winIt was found that it’s not possible to make the blue win in the case shown below, whatever way …6 answers
- DIY Challenge 3: Five districts from 25 squaresThere are a total of 25 squares. We need to make 5 districts with 5 people each. We have 9 Blue…5 answers
- DIY Challenge 4: Prove it either wayIs it possible to make the blue win in this case? If not, can you prove why?…5 answers