Puzzle 9 and 10

[kunal naidu]

Hi all,

Hope you all had a wonderful Diwali. Here are 2 more puzzles to get you back in rythm.

9.Two students play a game based on the total roll of two standard dice. Student A says that a 12 will be rolled first. Student B says that two consecutive 7s will be rolled first. The students keep rolling until one of them wins. What is the probability that A will win?

10. A 12 by 25 by 36 cm cereal box is lying on the floor on one of its 25 by 36 cm faces. An ant, located at one of the bottom corners of the box, must crawl along the outside of the box to reach the opposite bottom corner. What is the length of the shortest such path?

Note: The ant can walk on any of the five faces of the box, except for the bottom face, which is flush in contact with the floor. It can crawl along any of the edges. It cannot crawl under the box.

Please do not post the solutions on this group or mail them to me. I will put up the solutions myself in a few days

Regards

Kunal Naidu

Final Year Undergraduate

IIT Bombay