Last winter I found myself locked out of my house because I couldn’t remember the 5-digit code to open the garage door. I used the following facts to get inside.
1. The second and third digits add up to 9.
2. The first digit is equal to the second digit cubed.
3. The sum of the third and fifth digits is the smallest number with exactly five divisors.
4. The fourth digit is equal to 6 times the second-to-last digit.
5. None of the digits repeat.
If we label each digit a, b, c, d and e, we get the following equations.
1. b + c = 9
2. a = b3
3. c + e = 16 (since 16 is the smallest number with five divisors – 1, 2, 4, 8 and 16).
4. d = 6 * d (The fourth and second-to-last digits are the same number, meaning d must be zero to satisfy the equation)
5. b must be zero, one or two (b can’t be three because that makes a=27, which isn’t a single digit). Zero and one result in duplicate digits (00907 and 11808 respectively) so the only remaining value for b is 2, giving us 82709 and warmth.
James makes a bet with Laura that he can use any name she can think of in a song she will recognize with the original lyrics. Laura takes him up on the bet and loses. What song did James sing to win?
I’m in an elevator with two other people. When it reaches the first floor, one person gets out and six get in. When it reaches the second floor, three people get out and twelve get in. At the third floor, five leave and nine enter. It rises to the fourth floor, one person gets on and the doors close. Suddenly, the elevator cable snaps and the car smashes to the ground. No one survives the fall, yet I’m alive and know exactly how many people go on and off the elevator at every floor. How is this possible?
It cannot be seen, cannot be felt,
Cannot be heard, cannot be smelt.
It lies behind stars and under hills,
And empty holes it fills.
It comes first and follows after,
Ends life, kills laughter.