# Off on a Tangent 19.03

### Hope Mathematics & Statistics Shirts Available

Hope Mathematics & Statistics department t-shirts are available to purchase for a limited time. For the low price of \$10 (paid at pick up) you can buy a shirt and become one of the cool kids at the Werf. Go to the link here to place an order. All orders are due Wednesday, February 17.

### Snow Art Mysteriously Appears on Campus

The mathematics-inspired snow art shown below appeared outside VanderWerf Hall recently. It has not been determined whether this was produced by aliens or some Hope students that haven’t been assigned enough homework yet. Either way, it is beautiful!

To see other examples of snow art produced by professional snow artist Simon Beck go here.

### Problem of the Fortnight

While we’re still uncertain whether the chicken or the egg came first, we are certain that this fortnight’s problem is one to crow about!  Sit on it for a while and see if you can hatch a solution!

Suppose you wish to know which windows in a 100-story building are safe to drop eggs from and which will cause the eggs to break.  We make a few assumptions:

• An egg that survives a fall can be used again.
• A broken egg must be discarded.
• The effect of a fall is the same for all eggs.
• If an egg breaks when dropped, then it would break if dropped from a higher window.
• If an egg survives a fall, then it would survive a shorter fall.
• It is not ruled out that the first floor windows break eggs nor that the 100th floor windows do not cause an egg to break.

If only one egg is available, then the experiment can be carried out in only one way: Drop the egg from the first floor, and if it survives the fall, drop it from the second floor; continue going up a floor at a time until the egg breaks.  In the worst case, this method would require 100 droppings. Suppose that two eggs are available.  What is the least number of egg drops in the worst case scenario you need to make in order to determine with certainty which floor is the last safe floor from which you can drop an egg?

You can find the solution here. (But don’t peek unless you’ve got an answer to check!)