Batch 3 - Class 197 - Lines of Action
Pre-Class Exercise
- (MCDiaries 1 - Chap 9 - 4) Nelli faces two doors, one which has 20 random numbers and another which has 21 random numbers. Nelli must pick one door, and of the random numbers behind that door, erase one number so that the sum of remaining numbers is even. Which door should Nelli pick to be able to always do this successfully?
- Answer: 21 door. There could be 20 odd numbers behind the other door. However, on the 21 door, if the sum of all 21 numbers is odd, there must be at least one odd number which can be removed; similarly if the sum is even, then there must be at least one even number which can be removed.
Attendance Aashvi, Anishka, Anshi, Rhea, Liza, Arnab, Vaazisht, Kushagra, Rehaan, Advay, Smiti, Angad
Class puzzles
Lines of Action
Initial layout
Lines of Action is played on a standard chessboard, with the same algebraic notation for ranks and files. Each player controls twelve checkers, which are initially arrayed as follows:
Goal
The object of the game is to bring all of one's checkers together into a contiguous body so that they are connected vertically, horizontally or diagonally.
Movement summary
- Players alternate moves, with Black having the first move.
- Checkers move horizontally, vertically, or diagonally.
- A checker moves exactly as many spaces as there are checkers (both friendly and enemy) on the line in which it is moving. For example, Black may open with c8-c6. Black's checker moves two spaces because there are two checkers in the line (c8-c1) in which Black is moving.
- A checker may jump over friendly checkers, but not over an enemy checker.
- A checker can capture (remove) an enemy checker by landing on it. Checkers cannot capture friendly checkers.
Strategy
Lets kids come up with strategy to win. For example
- Blocking opponent pieces on periphery by occupying the second row or column helps
- Getting yourself into periphery doesn't help
- Getting your pieces in the center helps - dont allow opponent pieces to come in middle
- Be careful not to leave the opponent with one piece (since the opponent wins)
- Towards end of game, person left with fewer pieces to connect may have an advantage
- Identify spots where both you and opponent can get connections from - control those as you get towards endgame
- Anticipate what your opponent is trying to do
Homework:
- (536Dudeney - 281) Two army motorcyclist, on the road at Adjbklmasdsj, wish to go to Bczrtswty, which are marked as A and B below. Pipipoff said" "I shall go to D, which is 6 miles, and then take the straight road to B, another 15 miles." But Sliponsky thought he would try the upper road by way of C. Curiously enough, they found that the distance either way was exactly the same. How far is A from C?
- Answer: 3(1/3) miles
References:
Mathematical Circle Diaries, Year 1, by Anna Burago