# A solution to the 2017 Heller Family Christmas newsletter math problem

This year’s Heller Family newsletter appears to be missing the main reason the 10s of thousands of people read the newsletter: the math problem.

Nice try, Bill.

For those less diligent, they might say “Aw, there is no geometry / math problem this year. Just a bunch of family photos and stories about New Jersey college basketball.”

But I will not be so easily fooled.

**First, the sequence of “numbers at this stage of our lives” is a giveaway**

- 70
- 48
- 18 (4)
- 14/13
- 7.9(15)
- 5
- 3
- 3
- 2
- 0

Why would you include numbers if it wasn’t to perform math problems? There’s really no other use for numbers.

**Second, the “newsletter” has three blank pages at the end**

Why would you include blank pages if it wasn’t to work on a math problem?

This is not subtle.

**Third, the number of people in each family photo is such a slap in the face:**

- 2
- 13
- 3
- 3
- 3
- 3
- 1
- 11

Which, if you convert into an alphabetic sequence (1 = A, B = 2, C=3…) you get “BMCCCCAK” = B 1400 (MCCCC in slightly awkward Roman numbers is 1400, and AK = Alaska is the 49th state. 1400+49 = 1449. And of course, the B is for “bhliain” which means year in Irish. So, “the year 1449.”

**In 1449, **Pope Nicholas V was elected by the Council of Basel. The Council of Basel, it is well known, was the only city in Switzerland to have a professor of mathematics. Again, clever, but not sufficient.

So this is clearly a math problem. Or as we would say in Australia, a maths problem.

**The problem**

Let’s revisit our sequence

- 70, 48, 18 (4), 14/13, 7.9(15), 5, 3, 3, 2, 0

First, the parenthetical numbers are just a distraction and can be discarded like the thin guise of a “family newsletter” hiding the maths problem.

This leaves us with:

- 70, 48, 18, 14/13, 7.9, 5, 3, 3, 2, 0

The 14/13 is irregular in the sequence, with the 14 being Bill’s number and not Kathy’s number. Assuming this is Bill’s math problem, we will choose 14.

- 70, 48, 18, 14, 7.9, 5, 3, 3, 2, 0

This sequence looks of course *nearly *familiar, and one of the most overused math sequences in the history of overused math sequences. In one quarter of university, ‘Fibonacci’ was the answer to at least three of the computer science final questions I had. No points for originality here, Bill.

The traditional Fibonacci sequence is:

Fib(x) = Fib(x-1) + Fib(x-2), where Fib (0) = 0, and Fib(1) = 1, or:

- 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ..

If we compare our series side by side,

- 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ..
- 0, 2, 3, 3, 5, 7.9, 14, 18, 48, 70

We are very close, but need to shift a bit, and look at the differences:

- We have a gap in the row B, which can be negated by the “1 larger” in row C.
- The “1 larger” in row D is also negated by the 0.1 smaller in row G, since they are an order of magnitude apart, and 10 in binary is 2, and being three spaces apart, 2³ = 8.
- For rows H though K, we have 1,3,14, 15 — combining rows H and I we get “13”, and so the hidden sequence within the sequence is 13, 14, 15, and so the answer to this year’s maths problem is a simple linear sequence of 13, 14, 15,…
**16**.

Solved.

Ah, but wait, not so fast. Buried deep in the puzzle is that there was a choice of two numbers — we chose 14 because that was Bill’s number, and 13 was Kathy’s number. And in the solution, the final sequence starts with 13.

13 appears *twice* then, once to be discarded, based on our assumption that this is Bill’s puzzle, based on the knowledge that all puzzles in the past have been Bill’s puzzles.

But 13 re-appears even after we’ve discarded it. It will not go away.

This is not simple coincidence.

In mathematics, if you see a contradiction, check your assumptions.

We discarded the 13 *based on the knowledge that all puzzles in the past have been Bill’s puzzles. *If we take the 13 instead of the 14, the series better matches the Fibonacci series. In this way 13 appears a third time, but renders the puzzle no longer a simple linear series and enters the domain of unsolvable mathematical challenges that will plague mathematicians for millennia to come.

So, we must face the truth, the inevitable conclusion:

*Kathy has been the author of the Heller Family math problems all along. The years of family newsletter math challenges has been a ruse. Our world is turned upside down. We have lost true North.*

Clearly this is a political statement about the current administration of the US Government.

Much like persecuted mathematicians of the middle ages, Kathy is broadcasting a message to all of us that the time for revolution is near.

Or, maybe it was just a family newsletter.