354 Frequently Asked Questions In Quantitative Finance
Snowflake Start with an equilateral triangle. Now stick on
to the middle of each side equilateral triangles with side
one third of the side of the original triangle. This gives
you a Star of David, with six points. Now add on to the
sides of the six triangles yet smaller triangles, with side
one third of the ‘parent’ triangle and so onad infinitum.
What are the perimeter and area of the final snowflake?
(Thanks to Gerasimos.)
The doors There are one hundred closed doors in a cor-
ridor. The first person who walks along the corridor
opens all of the doors. The second person changes the
current state of every second door starting from the
second door by opening closed doors and closing open
doors. The third person who comes along changes the
current state of every third door starting from the third
door. This continues until the 100th person. At the end
how many doors are closed and how many open?
(Thanks to zilch.)
Two thirds of the average Everyone in a group pays $1
to enter the following competition. Each person has
to write down secretly on a piece of paper a number
from zero to 100 inclusive. Calculate the average of all
of these numbers and then take two thirds. The winner,
who gets all of the entrance fees, is the person who gets
closest to this final number. The players know the rule
for determining the winner, and they are not allowed to
communicate with each other. What number should you
submit?
(Thanks to knowtorious and theFinancial Times.)
Ones and zeros Show that any natural number has a mul-
tiple whose decimal representation only contains the
digits 0 and 1. For example, if the number is 13, we get
13 × 77 =1001.
(Thanks to idgregorio.)
