You have two buckets. One holds exactly five gallons and the other three gallons. How can you measure exactly four gallons of water into the five gallon bucket?
Assume you have an unlimited supply of water and that there are no measurement markings of any kind on the buckets.
A clock. It runs all the time, it “sings” for hourly chimes, cuckoos or alarms, it doesn’t have a head (but does have hands) and you look a clock in the face to tell the time.
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.
Maya’s mother asked her to buy some stamps. The available stamps were 3 cents, 9 cents, 11 cents, 17 cents and 21 cents. Her mother asked her to buy eight each of three stamps and nine of each of the remaining two stamps. Unfortunately, Maya forgot which stamps she was supposed to buy eight and nine of. Luckily, her mother had given her $5, the exact amount required to buy the stamps. Which stamps did she buy?
We are four against the masses. We are trying to find the one who is the whole package. We sigh, we laugh, we frown while we hope that the next one will be the one. Who are we?