## Archive for October 22, 2016

### Math Millionaire Quiz

It’s hard to believe that *Who Wants to Be a Millionaire* has been on the air since 1999, isn’t it? Even harder to believe is the number of math questions that have been missed by contestants.

In this post, I’m going to share five questions that have appeared on *WWTBAM*, followed by a brief discussion. If you’d like to solve them before reading the discussion, or if you want to share the quiz with friends or students, you can download it:

Three of the five questions were answered incorrectly by contestants. In one case, the contestant polled the audience and received some bad advice. If I hadn’t put this collection together, I’m not sure I would’ve been able to identify which ones were answered correctly. So maybe that’s a bonus question for you: **Which two questions were answered correctly?**

I’m unquestionably biased, but I always feel like the math questions on *WWTBAM* are easier than questions from other disciplines. Then again, maybe a history major would think that questions about Eleanor of Aquitaine are trivial. But take these non-math questions:

- In the children’s book series, where is Paddington Bear originally from? (Wait… he’s not from England?)
- What letter must appear at the beginning of the registration number of all non-military aircraft in the U.S.? (Like most things, it’s obvious — once you know the answer.)
- For ordering his favorite beverages on demand, LBJ had four buttons installed in the Oval Office labeled “coffee,” “tea,” “Coke,” and what? (Hint: the drink wasn’t available when he was Vice President.)

My conjecture is that non-math questions generally have an answer that you either know or don’t know, but math questions can be solved if given enough time to apply some logic and computation.

Perhaps you’ll disagree after attempting these questions.

**1. What is the minimum number of six-packs one would need to buy in order to put “99 bottles of beer on the wall”?**

- 15
- 17
- 19
- 21

**2. Which of these square numbers also happens to be the sum of two smaller square numbers?**

- 16
- 25
- 36
- 49

**3. If a euro is worth $1.50, five euros is worth what?**

- Thirty quarters
- Fifty dimes
- Seventy nickels
- Ninety pennies

**4. How much daylight is there on a day when the sunrise is at 7:14 a.m. and the sunset is at 5:11 p.m.?**

- 9 hours, 3 minutes
- 8 hours, 37 minutes
- 9 hours, 57 minutes
- 8 hours, 7 minutes

**5. In the year she turned 114, the world’s oldest living person, Misao Okawa of Japan, accomplished the rare feat of having lived for how long?**

- 50,000 days
- 10,000 weeks
- 2,000 months
- 1 million hours

**Discussion and Answers**

**1.** Okay, really? Since 16 × 6 = 96, one would need 17 six-packs, **B**.

**2.** This is the one for which the contestant asked the audience. That was a bad move… 50% of the audience chose A, but only 30% chose the correct answer. Since 25 = 9 + 16, and both 9 and 16 are square numbers (9 = 3^{2}, 16 = 4^{2}), the correct answer is **B**.

**3.** It’s pretty easy to calculate $1.50 × 5 = $7.50. The hard part is figuring out which coin combination is also equal to $7.50. Okay, it’s not *that* hard… but it took Patricia Heaton a lifeline and more than 4 minutes.

**4.** My question is whether daylight is officially defined as the time from sunrise to sunset. Apparently, it is. That makes this one rather easy. From 7 a.m. to 5 p.m. is 10 hours, and since 11 and 14 only differ by 3 minutes, we need a time that is 3 minutes less than 10 hours: **C**, final answer.

**5.** Without a doubt, this is the hardest of the five questions. Contestants aren’t allowed to use calculators, so they need to rely on mental math. Estimates will do wonders in this case.

- Days: 114 years × 365.25 days/year ≈ 100 × 400 = 40,000 days
- Weeks: 114 years × 52.18 weeks/year ≈ 120 × 50 = 6,000 weeks
- Months: 114 years × 12 months/year < 120 × 12 = 1,440 months
- Hours: 114 years × 365.25 days × 24 hr/day ≈ 40,000 × 25 = 1,000,000 hours

Only the last result is close enough to be reasonable, so the answer must be **D**.

What’s amusing is that the contestant got the correct answer, but for the wrong reasons. For instance, he estimated the number of weeks to be 50,000, not 5,000. He then used that result to say, “It can’t be 50,000 days, because it’s about 50,000 weeks.” That’s using a false premise to arrive at a correct conclusion. On the other hand, I wonder how well I’d be able to calculate in front of a national audience with $25,000 on the line. Regardless of how he got there, he correctly chose **D**, to which host Terry Crews said, “You took your time on this. You worked it through. It’s what we all need to do in life sometimes. And that’s how you *win the game*!”

Should I ever become a question writer for *Millionaire*, I’d submit the following:

**Which of the following are incorrect answers to this question?**

- B, C, D
- A, B, C
- A, C, D
- A, B, D