Ace Your Maths Interview - TOP Questions & Answers

Explore optimal strategies for a three-roll die game: decide when to stop or roll again to maximize expected winnings, using thresholds and remaining rolls.

Compute the expected tosses to reach three heads in a row on a fair coin, using induction and a recursive approach to derive E1, E2, and E3.

Solve classic aeroplane seating problem: with 100 seats, the probability the last passenger sits in their own seat equals one half, since the last seat is either 1 or 100.

Learn to compute the expected number of loops when tying ends of 100 loose strings, using a recursive approach starting from two strings.

Derive that three random points on a circle form a triangle containing the center with probability 1/4 by analyzing the opposite arc and integrating over theta.

The lecture compares e^π and π^e by using logarithms and a function f(x)= x/(a log x), shows f is increasing for x<e and decreasing for x>e, concluding e^π > π^e.

Find the positive x that leaves remainders 1, 2, 3, and 4 when divided by 2, 3, 4, and 5 by using x+1 as a multiple and the lcm; x=59.

Show that for primes p > 3 yield p^2-1 = (p-1)(p+1); both factors are even, one divisible by 4, and 3 divides the product, so 24 divides p^2-1.

Determine the number of trailing zeros in 1000 factorial by counting factors of five through floor divisions (5, 25, 125, 625), totaling 249.

Count the digit 1 occurrences from 1 to 1 million by examining each digit place, assuming uniform digits 0–9, yielding six hundred thousand and one total appearances.

Compute the angle between the vertical baseline and each clock hand at 3:15 p.m. Conclude that the hour and minute hands are 7.5 degrees apart.

This lecture analyzes the rabbit staircase problem, derives X(n)=X(n-1)+X(n-2), and shows how the distinct topways form the Fibonacci sequence, with 10 steps yielding 89.

Solve a timing puzzle with two ropes that burn to measure 45 minutes. Burn both ends of one rope for 30 minutes, then burn three ends to add 15 more.

Examine a doubling every second puzzle: a lily pad area is full at 30 seconds, so a quarter full occurs at 20 seconds when you count backwards.

Start first with 6 and respond to each opponent's move with 11 minus their number to reach totals of 11, 22, 33, and 44, aiming for 50.

Estimate how many ping pong balls fit in a jumbo jet by using reasonable dimensions, compute cross sectional area and volume, then apply 15,000 per m³ for about 31.5 million.