Batch 2 - Class 301 - Prime Cubes
zoom: send meeting Id and password
Start recording
Preclass Exercise:
- (Geoffrey - 161 Modified) The sketch below shows the plan of industrial establishment with secret weapons. There are only three gates which are guarded. There is some information leakage, and they found this note supposedly written for the spy
"Meet me every tuesday at the corner near my office. Enter by northwest gate and take a different route each time. That gives you 210 choices".
The detectives presumed the spy would enter top left and would always move to the right or down, in order to be efficient. Which office occupant was leaking the information?
- Answer: this is same as ways of arranging a number of 1's in a bit string. Since 210 appears as 5th number in 11th row, it must be at intersection of 7th and 5th Street (there is only one such combination above - if it was a larger grid, there would be two possibilities)
Attendance: Anika, Aneesh, Vansh, Yatharth, Rhea Chadha, Ryan Chadha, Vivaan, Adyant, Nikhil, Aarushi, Ekagra, Kabir, Siddhant, Siddharth, Aarav, Ayush
Class Notes:
(Reference presentation link and journal paper)
Homework
- In a special chess game played on 10x10 board, a "Camel" can do a 1,3 move i.e. move 1 square in any direction, and then 3 squares in a perpendicular direction. Is it possible for the camel to move to an adjacent square through a sequence of moves?
- Answer: No. The camel always remains on the same colored square
References:
https://docs.google.com/presentation/d/17ATd60JJdasRpdtR4-3D5Qswa6EpOPUskV_NXDGqBo4/edit#slide=id.gba13bef342_0_0
Mathematical Puzzles, Geoffrey Mott-Smith
(Above powerpoint and journal article are available on dropbox)