Let’s review questions 1 and 2 from yesterday’s problem set:

An athlete has six trophies to place on an empty three-shelf display case. The six trophies are bowling trophies F, G, and H and tennis trophies J, K, and L. The three shelves of the display case are labelled 1 to 3 from top to bottom. Any of the shelves can remain empty. The athlete’s placement of trophies must conform to the following conditions:

  • J and L cannot be on the same shelf
  • F must be on the shelf immediately above the shelf that L is on.
  • No single shelf can hold all three bowling trophies
  • K cannot be on Shelf 2


If G and H are on Shelf 2, which of the following must be true?

1. K is on Shelf 1
2. L is on Shelf 2
3. J is on Shelf 3
4. G and J are on the same shelf
5. F and K are on the same shelf


Write it out like this:

Bowling: F, G, H
Tennis: J, K, L

  1. G H

(Conditions are italicized) Since G and H are bowling trophies, and no single shelf can hold all three bowling trophies, then F, a bowling trophy, can’t be on shelf 2.  Which means tennis trophy F must be on shelf 1 because it can’t be on shelf 3 if it’s to satisfy condition that F must be on the shelf immediately above the shelf that L is on.  Which means L, a tennis trophy, is on second shelf.  The answer is 2, tennis trophy L is on shelf 2.


If no tennis trophies are on Shelf 3, which pair of trophies must be on the same shelf?

1. F and G
2. L and H
3. L and G
4. K and J
5. G and H

(Question two is not related to question one, don’t build off of the first question).  If no tennis trophies are on third shelf, then tennis trophy L must be on second shelf and tennis trophy F must be on first shelf because F must be on the shelf immediately above the shelf that L is on.  Since J and L (both tennis trophies) cannot be on the same shelf, and L is on second shelf, J must be on first shelf because no tennis trophies can be on third shelf.   If tennis trophy K can’t be on second shelf, and no tennis trophy can be on third shelf, then it must be on first shelf.  So:

  1. K, J, F
  2. ?, ?, L

Answer is 4. K and J.

We’ll do the remaining questions tomorrow.

College Essay Writing Exercise Part II

Again, the University of Chicago essay prompt:

Joan of Arkansas. Queen Elizabeth Cady Stanton. Babe Ruth Bader Ginsburg. Mash up a historical figure with a new time period, environment, location, or occupation, and tell us their story.
—Inspired by Drew Donaldson, AB’16

Whom did you pick?  Whom or what did you mash it with?  I picked Soong Ching-ling and mashed her with the fictional Alfredo Linguini, the deuteragonist of the animated foodie film, Ratatouille.  Below is what I know about Soong (surname comes first in Chinese), edited from first version:

The Soong sisters grew up in early 20th century Shanghai.  The eldest, Soong Ai-ling, is known for her love of money, married the wealthiest man in China.  The youngest, Soong Mei-ling, is known for her love of power, married the leader of the KMT, the man who would become president of the Republic of China.  The middle sister, Soong Ching-ling, is remembered for her love of her country and she married revolutionary leader Sun Yat-Sen, the founder of modern China, against her family’s wishes.  Soong Ching-ling eventually broke with her family and joined the Communist Party, remaining in mainland China as her family fled to Taiwan to set up provisional government, aka Republic of China, at the conclusion of the civil war.  She died as one of the most revered political figures in the history of China.

So I’ve taken Soong out of China and into the animated world of Ratatouille, where she is not Soong Ching Linguini, daughter of Alfredo Linguini and his mistress Valentina Ching (not from movie, I made her up), daughter of an Italian seamstress and a Chinese textile manufacturer.

Now I write what I know about Alfredo Linguini and Valentina Ching:

Alfredo Linguini is a bumbling and sometimes kindhearted cook who, with the help of his rat friend named Remy, rises to become owner and chef of a prominent restaurant.  Alfredo’s real superpower is his ability to skate so in the end, he becomes a waiter on skates at the restaurant he and his wife Colette own, while his wife and pet rat, Remy, are the chefs. It was at his restaurant that he met the captivating Valentina Ching, a fashion designer and daughter of an Italian seamstress and a Chinese textile manufacturer.  Alfredo meets Valentina at her boutique and there they begin an affair that produces Soong Ching Linguini, a celebrated chef renown for her linguini alfredo.

Point is, just write, you can edit later.  We’ll finish this essay tomorrow.