Another way to improve Math skills is to practice solving logic problems.  Here’s a set of LSAT (Law School Admissions Test) problems made up by Kaplan, a leading test prep center:

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

Question 1

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

Question 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 3

If J is on shelf 2, which of the following must also be on Shelf 2?

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

Question 4

If Shelf 1 remains empty, which of the following must be FALSE?

1. H and F are on the same shelf
2. There are exactly three trophies on Shelf 2
3. G and H are on the same shelf
4. There are exactly two trophies on Shelf 3
5. G and K are on the same shelf

Question 5

If L and G are on the same shelf, and if one of the shelves remains empty, which of the following must be true?

1. If H is on Shelf 3, then J is on Shelf 2.
2. K and L are on the same shelf.
3. If H is on Shelf 2, then J is on Shelf 3.
4. F and K are on the same shelf.
5. If J is on Shelf 2, then H is on Shelf 1.


We’ll review some of the questions tomorrow.  Tip: use a pencil and a notebook to sketch the question.  It’ll help you visualize the problem.

Advanced Essay Writing

Here’s a playful college admissions essay prompt, from The University of Chicago:

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

What’s the first step?  For me, I list historical figures who intrigue me.  Here’s my list, I limited it to nine:

  • Lee Kuan Yew
  • Malcolm X
  • Peter Abelard
  • Soren Kierkegaard
  • Joan of Ark
  • Bathsheba
  • Soong Ching-ling
  • Ching Shih
  • Franz Fanon

The one I really want to write about is Soong Ching-ling.  Next I write down what she’s known for.

The Soong sisters grew up in early 20th century Shanghai.  The eldest, Soong Ai-ling, is known for her love of money, so she married the wealthiest man in China.  The youngest, Soong Mei-ling, is known for her love of power, so she 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.

The point is to keep it simple and write write write. Don’t think too much, and less is more.

Now we have to fuse her with something or another.  I’m open to anything, time, location, another person, I don’t mind.  I’m going to use the search engine for ideas.  I search for: “words that begin with ling.” That takes me to a site that lists many words that begin with “ling.”  Here are a few that intrigue me:

  • lingerie
  • lingua franca
  • linguini
  • linguistics

Next I search: “cities that begin with ling.”  I go to site with list but don’t find anything interesting, only a few small cities, all but one in China.  I’m going to pick “linguini” then and make this a foodie story.  I check to see if there’s anyone named Linguini and sure enough, the fictional Alfredo Linguini, the deuteragonist of the animated foodie film, Ratatouille.  So, I introduce:

Soong Ching Linguini, the daughter of Alfredo Linguini and his mistress Valentina Ching.

We’ll add to this story tomorrow.  Where are you at in your story?