Question: A photon starts moving in the random direction from the center of the square of size 3. Letâ€™s say it first colloids to the glass wall AB. What is the expected distance traveled by the photon before hitting the wall AB again? . . C A P T A I N I N T … Continue reading Lumos

# Category: Mathematical

# Chameleons go on a date

Question: On an island live 13 purple, 15 yellow and 17 maroon chameleons. When two chameleons of different colors meet, they both change into the third color. Is there a sequence of pairwise meetings after which all chameleons have the same color? . . C A P T A I N I N T E … Continue reading Chameleons go on a date

# Four points in a sphere

Question: Consider a unit sphere. 4 points are randomly chosen on sphere, what is the probability that the center (of the sphere) lies within the tetrahedron (polygon) formed by those 4 points? . . C A P T A I N I N T E R V I E W . . Solution: Let A, … Continue reading Four points in a sphere

# 100 balls

Question: You are given an urn with 100 balls (50 black and 50 white). You pick balls from urn one by one without replacements until all the balls are out. A black followed by a white or a white followed by a black is "a colour change". Calculate the expected number of colour changes if … Continue reading 100 balls

# Strings

Question: You have a bag with 'N' strings in it. You randomly grab two ends and tie them together until there are no more loose ends. In the end, what is the expected number of loops (strings tied to their own end)? . . C A P T A I N I N T E … Continue reading Strings

# Elementary mathematical functions

Question: Is it possible to make 5 with only two 2's using only elementary mathematical functions? . . C A P T A I N I N T E R V I E W . . Solution: