Answer to Math Problems in Seclusion, 29 March 2020

1. How many mathematicians does it take to change a lightbulb?

Answer: It takes three—one to install the lightbulb and one to confuse the students.

2. If a hen and a half can lay an egg and a half in a day and a half, how long does it take three hens to lay three eggs?

Answer: It takes a day and a half. The question is a confusing way of saying one hen can lay one egg in a day and a half.

3. How far can you run into the woods?

Answer: You can run in halfway. After that you are running out.

4. Which weighs more, a pound of feathers or a pound of gold?

Traditional Answer: Neither, they both weigh the same, namely one pound.

Technically Correct Answer: Our society uses different units of weight to measure mundane objects like feathers from those it uses to measure precious metals like gold. We measure everyday objects using avoirdupois weights and precious metals using troy weights. As it turns out, it takes about 1.2 pounds troy to equal 1 pound avoirdupois. Thus, the pound of feathers is heavier.

5. What is the next number in the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, …?

Answer: The next number is 89. In this sequence each number is the sum of the two before it. For instance, the sixth number of the sequence is the sum of the fourth and fifth numbers: 3+5 = 8. Thus, the next number in the sequence is 34 + 55 = 89. This sequence constitutes the famous Fibonacci numbers (you may have heard of them), named after the greatest medieval mathematician, Leonardo of Pisa, who lived AD 1170–1240. (He received the nickname Fibonacci centuries after the end of his life). He used these numbers to solve a (highly contrived) problem about the growth of a rabbit population.

6. How long ago did the equals sign “=” first appear?

Answer: The equals sign first appears in the book The Whetstone of Witte, an algebra text that the Englishman Robert Recorde published in 1557. Thus, the equals sign first appeared 463 years ago.

7. Choose a four-digit number (any one you like) with no digit repeated (for example 4729). Rearrange the digits of this number (however you like) into a different four-digit number (for example 2794). Subtract the larger of these numbers from the smaller. Divide the difference by 9. What is the remainder?

Answer: Regardless of the number you choose to start with, the remainder is zero. For example, the difference 4729 − 2794 = 1935 is divisible by 9 since 1935 ÷ 9 = 215 with no remainder. Accountants use this fact to help find the source of errors when numbers don’t add up. If the error is divisible by 9, there is a good chance that someone transposed the digits of a number (wrote them in the wrong order) somewhere.

8. One of the world’s oldest riddles seems to make its first appearance in an Egyptian papyrus (the Rhind Mathematical Papyrus) dating back to 1650 BC. It first appears in English in the eighteenth century (the 1700’s) in a form similar to the following. What is the answer to the riddle?

As I was going to St Ives,

Upon the road I met seven wives;

Every wife had seven sacks,

Every sack had seven cats,

Every cat had seven kits:

Kits, cats, sacks, and wives,

How many were going to St Ives?

Traditional Answer: I was going to St. Ives. I met the other folks going the other way. So, one was going to St. Ives, namely I.

Another Answer: Going to St. Ives, I overtook the other folks. Thus, I was going along the 7 wives, the 7 times 7 sacks, the 7 times 7 times 7 cats, and the 7 times 7 times 7 times 7 kittens. Adding this all up we get 1 + 7 + (7 × 7) + (7 × 7 × 7) + (7 × 7 × 7 × 7) = 1 + 7 + 49 + 343 + 2401 = 2801 going to St. Ives.

Another Answer: The questions is specifically about “kits, cats, sacks, and wives.” In the first scenario above (they are going away from St. Ives), none of them is going to St. Ives, meaning the answer is zero.

Yet Another Answer: The questions is specifically about “kits, cats, sacks, and wives.” In the second scenario above (they are going toward St. Ives), we get the same answer as before except that I (the narrator) am excluded. In this case there are 2801 − 1 = 2800 going to St. Ives.