Did you solve it? Art thou smarter than Shakespeare?

Photograph: Akademie/Alamy

Earlier today I set you these puzzles, set by the author of Much Ado About Numbers, a new book about mathematics in Shakespeare’s day.

1. Hours and hours

How many hours are there in a week? And when you’ve worked it out, can you now figure out how Shakespeare expressed that number in words? He did it using only 15 letters, true to his line “Brevity is the soul of wit.”

Solution 168 = “eight score eight” (Bianca states this number in Othello)

2. Duke of hazard

Hazard was a gambling game with dice that was one of the most popular recreations in Elizabethan England. Shakespeare refers to it indirectly several times. Usually two dice were involved, but sometimes three – which threw up this question, a particular source of debate at the time.

Three dice are thrown. Which total is the more likely (and thus a better bet)?

a. Nine

b. Ten

c. Nine and ten are equally likely.

Solution b

There are 27 ways to score 10 and only 25 to score 9, so 10 is the better bet. Common belief among players at the time was that there were only six ways to get 9 (1-2-6, 1-3-5, 1-4-4, 2-2-5, 2-3-4 and 3-3-3); and six ways to get 10 (1-3-6, 1-4-5, 2-2-6, 2-3-5, 2-4-4 and 3-3-4) so the chances were believed to be equal. Galileo revealed the fallacy in around 1620.

3. Hard to fathom

Shakespeare uses all of the following measurements of distance: a mile, a league, a fathom and a furlong.

Can you list them in order of size?

Solution

1. a league. Although not an official measure, a league is roughly the distance you can walk in an hour, i.e. three miles. (Jules Verne’s “20,000 leagues under the sea” is one of the more absurd book titles, given that the earth’s diameter is less than 3,000 leagues.)

2. a mile

3. a furlong is 220 yards (about 200m).

4. a fathom is six feet (about 2m

4. Twin twister

The plot of Twelfth Night revolves around non-identical (fraternal) twins Sebastian and Viola. The perfect excuse to set this classic puzzle about birth-adjacent siblings:

A 17th century farmer observes that one of his sheep is pregnant. As all famers know, lambs arrive as non-identical twins, each with a 50-50 chance of being male or female. The local vet has an Elizabethan ultrasound machine and finds out the genders of the lambs: “Is it true that at least one of them will be male?” asks the farmer. “Yes, it is true” replies the vet.

“In that case,” the farmer says, “the other one will most likely be female”. Is the farmer correct?

Solution Yes!

There is a 2/3 chance that one of the lambs will be female. If we know that at least one lamb is male, then the possible pairings of the first and second lamb are male-male, male-female and female-male, and each of these pairings is equally likely. There will be a female in two of the three scenarios, hence the 2/3 probability.

As an interesting aside, Shakespeare himself was the father of fraternal twins, Hamnet and Judith – we shouldn’t be surprised that they were a boy and a girl.

Much Ado About Numbers by Rob Eastaway is out on Thursday 18 April and can be bought on the Guardian Bookshop or other online retailers.

I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.