The SexAT, Circa 781

Several years ago when I was preparing to take the SAT, I proposed the idea of the SexAT, a new test prep book specifically designed to appeal to high schoolers.  I would take existing SAT questions and simply reformat them into something more interesting and relevant.  Here’s how I would revise one of the hated problems on proportions and ratios.

Existing boring example that everyone hates:

The price of a telephone was first increased by 10% and then the new price was decreased by 25%.  The final price was what percent of the initial price?

New exciting and relevant revision in the bestselling SexAT:

Your fraternity house is hosting a party and wants to make a mixed drink out of vodka and juice.  Paul, the first taste tester, says the mixture was too weak, and he added 10% more vodka.  Sam the second taste tester, said the mixture was too strong so he added 25% water.  The final mixture was what percent of the initial? 

The section on grammar features poorly written sentences, with suggestions on how to rewrite them.  The content of the sentences themselves are basically irrelevant, so they can be easily revised as follows:

Existing boring example that everyone hates:

“Confident that she was fully prepared, Ellen decided to spend the night before the recital reading and relaxing but not to be practicing.”

New exciting and relevant revision in the bestselling SexAT:

“Confident that he was fully prepared, Tom decided to spend the night before the prom updating his Facebook page, but not to be making sure that he had checked his supply of condoms.”

My enthusiasm for this project is largely based on the catchy title, which I think is half the battle in a book sale.  When my son was a high school senior, I remember buying a book called, “Harvard Schmarvard,” which had something to do with the college admissions process, and when he was renting an apartment at college, I bought him a cookbook called “Everyone Loves Ramen.”  Both books were purchased based on the title alone and saw little action.  I have even gone so far as to trademark the term SexAT™ so that nobody can rip me off.

At the same time that I was mulling this project over, I renewed my interest in Math, and specifically in the history of math, as I wanted to find the answer to a question that had troubled me since high school. How do you multiply and divide Roman numerals?  The answer was, as I already suspected, you really can’t.  The introduction of our current Hindu-Arabic system of numbers solved these problems, except that the concept of an equation, with an equal sign, and symbols for multiplying and dividing wasn’t accepted until sometime later.  This meant that all math consisted of word problems.  One of my reference books described the first known collection of word problems, published in the eight century.  This was my first eureka moment.  Students have been struggling with the same basic word problems for over a thousand years.

Alcuin of York was a notable scholar during the reign of Charlemagne and in 781 the king appointed him his education advisor.  During this period, he created the first math “textbook” titled “Problems to Sharpen the Young.”  The book consists of 56 problems, illustrating 9 different types of problems, all of which can still be found on the SAT test.  One category is called “heap problems,” illustrated by problem 2 in Alcuin’s text:




“A man saw some horses at pasture, and wished they were his, and that there were others with them that were his, the same number again, plus a quarter of the sum that would result, for then he would glory in 100 horses.  How many did the man see at pasture?”

You can count on at least one of these “heap” problems in the SexAT, perhaps involving invitations to prom after parties instead of horses.  Another category is called the “hundred fowls,” apparently since the first example of this type of question was actually found in 5th centuryChina.

A merchant wanted to buy a hundred pigs for one hundred pence.  For a boar he would pay 10 pence; and for a sow 5 pence; while he would pay one penny for a couple of piglets.  How many boars, sows and piglets must there have been for him to have paid exactly 100 pence for 100 animals?

Alcuin has substituted pigs for fowls, but in my SexAT I would substitute illicit substances for pigs.  “Strange family” problems are more like brain teasers, along the lines of:  if two men each take the other’s mother in marriage, what would be the relationship between their sons?  In this strange family you could be your own grandfather.  Then there are many geometry problems, such as how many swine can fit into a stall, or how many casks of wine can fit into a cellar.

My second eureka moment came as I read the first of many “river crossing” problems.  This was the moment when Alcuin validated my concept of the SexAT, across a span of 1231 years.  Here is the problem:

“Three friends, each with a sister needed to cross a river.  Each one of them coveted the sister of another.  At the river they found only a small boat, in which only two of them could cross at a time.  How did they cross the river without any of the women being defiled by the men?”

The choice of the word defile is absolutely charming.  You get this great visual image of rocking boats with water slopping over the sides and giddy maidens being pursued through swaying riverside grasses.  Now clearly Alcuin could have chosen any combination of people for his problem, for example an obese family, where you would have to figure out how to get them all across without sinking the boat and without leaving a child alone.  In fact throughout history, this same basic problem has been reformatted to reflect the issues of the time.  For example, during the Reformation the boat could be filled with Catholics and Protestants and during the colonization of Africa, the boat could be filled with trembling missionaries and eager cannibals.  But Alcuin was brilliant.  By choosing the eternal issue of sex, he avoided any specter of political correctness, treason or blasphemy.  And by creating a sexual context, I’d like to think that both Alcuin and I were addressing the same problem – we both needed to spice up the questions to motivate students.

Many of us have experienced the challenges of motivating our high school children, hoping that they will take the SAT or ACT test seriously.  Alcuin was probably no different.  Here is the year 781 version of this timeless conversation, featuring the overweening mother Betrada and her sullen son Pepin.  (Please note the use of pretentious words throughout as I would also like to imagine that in his river crossing problem, Alcuin’s choice of the word “defile” is a nod to multitasking with vocab practice.)

Betrada watches Pepin slouch in the corner, idly picking ticks off the household dog and throwing them into the blazing hearth.  “Son, I beseech thee, why would you not spend time with these reckoning problems that your kindly uncle Alcuin has left for you?”

Without looking at his mother, Pepin says, “I find these problems most noisome, such as reckoning the number of swine that will fit inside a stall, and I have heard such discussion at the ale house where wagering men find much amusement, but I think that ‘twould be much simpler to ask neighbor Lombard, since he has such a stall filled with pigs.”

“Ale house, did you say ale house?  I have told you that you are much too young to be visiting those houses of ill repute.  I pray that you have not overimbibed and brought condemnation upon our household,” sighs Betrada.  Seeing no response from Pepin, she continues, “You know how important it is to get a position at the court of Charlemagne.  He is a mighty king of great intellect, and you can continue your education there.”

“Why should I not go to the school just down the road?” asks Pepin.

 “By my word, you know so little of the world.  If you stay here, you can only become, at best, an apprentice cobbler. Your future will be secured if you get a position at court, and our future depends on it also.  Your sister’s prospects for marriage will improve if you are at court.  We have a great legacy at the court, your father, God rest his soul, your father’s father and his father before him all served our kings, but I am told that this record is no longer adequate and that Charlemagne is only seeking men with nimble and agile minds.  You know your younger cousin Adalbert got a position at court last year, and you have so many more gifts.  Your tutor will attest to your fine art and poetry, your words and penmanship.  But he cannot be so fulsome about your reckoning skills.”

“Dear mother, everyone knows why Adalbert got a position at court, though he is only of middling intellect.  King Charlemagne has announced that he is seeking scholars from all quarters of his realm.  Adalbert is fromWest Woppingshire, a town that has never sent a scholar to court.  I am fromOxford, where there are many scholars, and Charlemagne does not seek any others from here.  I fear that my geography is working against me.”

“Pepin you cannot give up.  Alcuin has told me that the King has asked him to devise a great test to identify the most nimble minds, and these scholars will be appointed to the court, and given an apartment and they can feast at the King’s great table.  These problems that your uncle has so kindly given you are examples of the very problems that will be on the test.  He told me, ‘Have Pepin study them well and surely he will find great success.’  “Here take a look at this one,” said Betrada, “this one is about men and women defiling each other in a boat.”

“Zounds,” exclaims Pepin,” as he grabs the sheaf from his mother, and rushes off to study.  Two months later he learns that he is the first scholar to ever score an 800 on Alcuin’s test.  He is appointed to court as the assistant to the exchequer, his sister marries a wealthy landowner, his mother becomes a lady in waiting, and his uncle Alcuin publishes the first test prep book to great acclaim.

The missing words in the following poem are anagrams (i.e. share the same letters like spot, post, stop) and the number of asterisks indicates the number of letters.  Your job is to solve the missing words based on the above rules and the context of the poem.  Scroll down for answers.

When the waters **** high and the river is wide,

The farmer works to get his flock to the other side

On the first trip he had to leave behind some of his ****

But from both sides of the river he heard a long hungry howl.

A **** and some chickens, it’s a classic problem of the river crossing kind

That has been vexing students since Alcuin tried to sharpen the mind.










Answers: flow, fowl, wolf

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