 # Mathematical fanatical: How to turn ‘1’ into ‘2019’?!

Hi folks!

2019. Is it two thousand nineteen, or twenty nineteen? How does it sound to you? “It’s just a number – the number of the year,” you say? Hmm. I think your saying that might mean poetry or just rhythm-and-rhyme aren’t your fortes. Right? For – and not a lot of people know this – there’s a phenomenon known as digital poetry. There are all different kinds of digital poetry, as a quick glance at that Wikipedia page will show you. One kind I find rather intriguing is the one where numbers are substituted for the words of the works of the great poets – and you need to work out who that poet is based on the way the numbers are pronounced – which words are stressed, the number of syllables, and so on.

Here, for example, are some numbers that, when spoken, reflect the poetry style of Alexander Pushkin (at least, in Russian:):

17 30 48
140 10 01
126 138
140 3 501

I wonder, does it work the other way round? I mean, can a poem be made up about 2019? Might there be some budding digital poets among you, dear readers, who might be able to conjure up a poem about 2019?

Meanwhile, for the mathematicians and physicists among you, my traditional annual arithmetic puzzler…

I hope you remember the rules. If not:

You need to get the number of the current year – this year being 2019 of course – using the four main arithmetic operations [+, -, *, ÷], plus parentheses [(, )’], and the figures 10, 9, 8, 7, 6, 5, 4, 3, 2, and 1; and not in any order but in the order given [10 down to 1] – and with no joining up of the numbers to make bigger numbers (e.g., 1 and 2 making 12).

For example:

((10 + 9 – 8) * 7) + (6 + 5) * (4 – 3 + 2) + 1 = 111

Hmm. That gives 111. But I wanted 2019.

All righty. Try it! Who does it first is the winner!

10 9 8 7 6 5 4 3 2 1 = 2019
…

Did you do it? Well done!

Now, let’s continue the fun by upping the difficulty a bit: let’s drop the 10:

9 8 7 6 5 4 3 2 1 = 2019

Now let’s drop the 9:

8 7 6 5 4 3 2 1 = 2019

You managed it?

Now drop the 8.

Now the basic arithmetic is catastrophically lacking. So from here onward (rather – downward) – factorials, degrees, roots, elations, and other logarithms can be used. A little further (from 6 down) you’ll need multiple, sub-, and super-factorials. From 5 on down I needed special numbers like: a Leonardo number, a Fermat number, a Fibonacci number, a Catalan number, and a Mersenne prime, no less.

7 6 5 4 3 2 1 = 2019
6 5 4 3 2 1 = 2019
5 4 3 2 1 = 2019
4 3 2 1 = 2019

Now, surely you can’t get to a year in the two-thousands from just the last three figures? From two? Actually, it’s possible! I should know as I’ve managed it before!

3 2 1 = 2019
2 1 = 2019

And for the icing on the cake: how do you get 2019 from… 1?! Joke! Mathematical space and time isn’t made-up sci-fi Hollywoodness; everything obeys strict, logical laws. Magical teleportation of 1 to 2019 isn’t going to happen (at least not in our lifetimes). That’s clear and obvious… and also not true!!

There are, at a minimum, two ways of getting to 2019 from 1 all on its lonesome. The first is a trigonometrical caterpillar, kinda like ‘ctg arctg sin arcctg‘. If you apply it the required number of times you get an arbitrary natural number. Yes, really! This method was first used back in January 2017. Last year, I managed to get to 2018 from 1 by transforming it via a Fermat number, a Woodall number, an antisigma (there is such a thing, though the internet seems to not be aware!) and multiple factorials.

Actually, use of such a special function as an antisigma could be regarded as cheating. If you dig around a bit, you’ll probably find this or that ‘craft’ mathematical function that in a particular case gives you the number 2019. All you have to do is add the necessary ‘fuel’, and that’s it – done.

Accordingly, this time I’m making things more difficult:

You need to get to 2019 from just one ‘1’ – using only ‘widely known’ mathematical functions and actions; that is, those on which there is at least a Wikipedia page! No esoteric para-mathematical stuff! Also forbidden is using a trigonometrical caterpillar or any derivatives thereof, since such a construction has already been contrived and is universal.

Ok. So all you mathematicians among you – off you go!…

1 = 2019

Good luck!… #### Brul

What I tried, using ln, cosh, sinh and tan, floor and ceiling:

(1) Note that floor(ln cosh N) = N-1. Proof is straightforward computations leading to exp(N-1) < cosh N < exp(N). This is main idea used for "fine-tuning", but without making hundreds of steps.

(2) Similarly, floor(cosh ln N) around N/2; don't need to be precise.

(3) Now some guesswork to reach 2019 in few steps.
ceiling (tan(tan(1)) = 75
ceiling (sqrt 75) = 9
floor (sinh 9) = 4051
Now divide by 2 as per idea (2), then repeat idea (1) 6 times to substract 6, ending up at 2019.

Hope I did no mistakes, checked with excel up until 2025. #### Edvard

but, what about the rules?, “…and the figures 10, 9, 8, 7, 6, 5, 4, 3, 2, and 1; and not in any order but in the order given [10 down to 1] …” #### Uschi

The year 2019
I am no mathematician , as you may notice , just answering your question in the Uschi style…)

As time is relative , time in itself is elusive. However as all things are in existence, the number zero can not apply. To emphasise existence, existence can ever be only defined as a number one as an on going state of existence . ( A line stretching forward) Therefore all things which exist are ever in existence (one) as long as existence exist…’one’ existence on going until nothing exists, which would end in zero…

:)

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