## Archive for March, 2018

### Fortune Bank Teller

One of the radio commercials in the GEICO “Surprising” campaign features a **fortune bank teller** who dispenses both greenbacks and prognostications. The commercial ends with the teller saying,

I see a yellow light serpent… and a low APR.

What you may also find surprising is that this commercial reminds me of my father-in-law, Julian Block, a nationally known tax expert. Julian used to work for a company that connected advisors to people seeking help. An operator would ask a few questions of each caller and then connect the advisee with an appropriate consultant. Sometimes, however, the advisee would be connected to the wrong expert. And the problem? The company specialized in dispensing two types of advice: tax and psychic.

You may now see why the GEICO commercial reminds me of my father-in-law. When calls were incorrectly routed to him, he would become a de facto **psychic tax advisor**. I imagine conversations like the following:

Young Woman: My boyfriend just proposed. Should I marry him?

Julian: That depends. What’s his tax bracket?

These combinations — fortune teller and bank teller; psychic advisor and tax advisor — yield rather whimsical new professions. It made me wonder if there were others. Sadly, an hour of brainstorming yielded only a handful of satisfactory results:

**Super Hero Intendent**, who still has time to fight crime after 8 hours of dealing with stopped-up toilets

**Dog Street Walker**, who thinks the oldest profession is picking up Spot’s poo

**Antique Debt Collector**, who will accept payment in Ming vases and pocket watches

**Switchboard Lottery Operator**, who has a 1-in-500 chance of connecting you to the right person

**Social Construction Worker**, who can strike up a conversation with anyone while shingling a roof

**Foreign Language Flight Instructor**, who will teach you how to land safely after you give her the declension for *agricola*

Got any others you’d add to the list? Post them in the comments.

### Stick Figure Math

I’ll never forget the first time I saw the pattern

1, 2, 4, 8, 16, __

and was dumbfounded to learn that the missing value was **31**, *not 32*, because the pattern was *not* meant to represent the powers of 2, but rather, the number of pieces into which a circle is divided if *n* points on its circumference are joined by chords. Known as Moser’s circle problem, it represents the inherent danger in making assumptions from a limited set of data.

Last night, my sons told me about the following problem, which they encountered on a recent math competition:

*What number should replace the question mark?*

Well, what say you? What number do you think should appear in the middle stick figure’s head?

Hold on, let me give you a hint. This problem appeared on a multiple-choice test, and these were the answer choices:

- 3
- 6
- 9
- 12

Now that you know one of those four numbers is *supposed* to be correct, does that change your answer? If you thought about it in the same way that the test designers intended it, then seeing the choices probably didn’t change your answer. But if you didn’t think about it that way and you put a little more effort into it, and you came up with something a bit more complicated — like I did — well, then, the answer choices may have thrown you for a loop, too, and made you slap your head and say, “WTF?”

For me, it was Moser’s circle problem all over again.

So, here’s where I need your help: **I’d like to identify various patterns that could make any of those answers seem reasonable.**

In addition, I’d also love to find a few other patterns that could make some answers other than the four given choices seem reasonable.

For instance, if the numbers in the limbs are *a*, *b*, *c*, and *d*, like this…

then the formula 8*a* – 4*d* gives 8 for the first and third figures’ heads and yields 8 × 6 – 4 × 9 = **12** as the answer, which happens to be one of the four answer choices.

Oh, wait… you’d don’t like that I didn’t use all four variables? Okay, that’s fair. So how about this instead: ‑3*a* + *b* + *c* + 2*d*, which also gives ‑3 × 6 + 7 + 5 + 2 × 9 = **12**.

Willing to help? **Post your pattern(s) in the comments.**

[**UPDATE (3/9/18):** I sent a note to the contest organizers about this problem, and I got the following response this afternoon: “Thanks for your overall evaluation comments on [our] problems, and specifically for your input on the Stick Figure Problem. After careful consideration, we decided to give credit to every student for this question. Therefore, scores will be adjusted automatically.”]