Two guards were on duty outside a barracks. One faced up the road to watch for anyone approaching from the North. The other looked down the road to see if anyone approached from the South. Suddenly one of them said to the other, “Why are you smiling?”
Farmer Finnegan needs to build a fence to keep his horses on his property. He only has a little over 1.5 miles of fence materials, but there’s also a mile-long straight river running through his property. What shape should he use for the fenced in area to give his horses the most space possible?
Our dear friend Finnegan should build a half-circle fence with the river as the diameter, giving the horses about 0.4 square miles to frolic and play in.
Area of semi-circle = πr2 / 2 = π × .5 miles2 / 2 = 0.3927
It cannot be seen, it cannot be felt,
Cannot be heard, cannot be smelt,
Lies behind stars and under hills,
And empty holes it fills.
Comes first follows after,
Ends life kills laughter.
I have palms but not on hands,
I offer foods from distant lands,
When at my peak you’ll see me smoke,
I’m famous for my friendly folk,
My flowers grow and yet they lay,
There’s fire where a man will play,
I’m sure you know we’re family,
You’re welcome to come stay with me.
You’re waiting to board your flight at the airport with 99 other passengers, each with an assigned seat. All but one of the passengers will gladly sit in their designated seat. The only exception is Randall, a scoundrel who refuses to follow the rules. When he boards, he will choose a random, unoccupied seat.
If a rule-following passenger finds someone in their spot, they will choose another one at a random from the remaining unoccupied seats.
What is the probability that the last person to board the plane will sit in their proper seat?
The randomness stops as soon as someone else sits in Randall’s assigned seat. The chances of this happening range from 1 out of 99 to 1 out of 1 (when only one seat remains).
Thus, the probability of the last person sitting in their own seat can be calculated as 1/99 plus the sum of 2 to 98 of the formula 1 / n × (n + 1), which works out to 0.5, or 50%.
So there’s a 50% chance the last passenger will sit in their own seat thanks to Randall for screwing up order and procedure when boarding an aircraft.