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"Write a number", said Grandpa

"Which is the shortest number, that is also the largest"

"Shortest?" I asked

"Yup. You can write it with six straight lines, period"

"So you want me to write a shortest largest number?"

Grandpa nodded with a smile, " It is an integer way over a billion too"

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    $\begingroup$ I’m voting to close this question as off topic because, as it is when this comment was posted, it does not contain enough specification to identify a single most correct answer, as evidenced by the numerous equally valid answers currently $\endgroup$
    – HTM
    Oct 21, 2019 at 19:01
  • $\begingroup$ Although this is closed, is the answer ... rot13(n ebzna ahzreny, creuncf Z jvgu bireyvarf)? $\endgroup$
    – athin
    Oct 22, 2019 at 0:24
  • $\begingroup$ Great @athin! M overline Factorial. $\endgroup$
    – DrD
    Oct 23, 2019 at 19:49

8 Answers 8

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Grandpa tells us that we can use six straight lines and a period, so: 11,111!
According to Wolfram Alpha, the approximate decimal value of 11111! is 2.18375673134769091609082425627986195737914744897617... × 10^40129.. which is an integer considerably more than a billion! In fact, more than a billion billions! Or a billion billion of billions! (and so forth and so on for pretty much as long as you want to go multiplying billions together).

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    $\begingroup$ I suspect that this slightly strange reading of the question isn't what was intended. $\endgroup$
    – Trevor Powell
    Oct 21, 2019 at 10:24
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    $\begingroup$ Oh, that's good, I never thought of using the period like that! $\endgroup$
    – ThatOneNerdyBoy
    Oct 21, 2019 at 10:26
  • $\begingroup$ The thing that really kills my answer, at least for me, is that it's not actually a number, which seems to be what the question is asking for? Instead, it's an expression that evaluates to a number. And I sort of feel like that's not what the OP was looking for. (this is true of a bunch of the other proposed answers too, though) $\endgroup$
    – Trevor Powell
    Oct 21, 2019 at 11:02
  • $\begingroup$ Good lateral thinking but is it really the shortest in terms of writing? $\endgroup$
    – DrD
    Oct 21, 2019 at 12:12
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    $\begingroup$ Check my updated answer :D $\endgroup$
    – Conifers
    Oct 21, 2019 at 16:01
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The greatest one I could think of is

$^{111!} 11$
which means $11^{11^{^{.^{.^{11}}}}}$ repeated $111!$ times using tetration. (No software can approximate this)

EDIT

Along the same track, I thought of a better one:

$^{^{11} 11} 11$ which is just plain incomprehensible.

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    $\begingroup$ Tetration wins here probably because pentation takes too many lines to write $\endgroup$
    – Avi
    Oct 21, 2019 at 18:53
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My answer would be:

$77^7$

It can be written in six straight lines:

enter image description here

It is an integer way over a billion, too:

$77^5$ is already well into the billions, so $77^7$ definitely fits the criteria!

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    $\begingroup$ you do the thing once. Wouldn't you get a much larger number by doing the thing twice? $\endgroup$
    – Ben Barden
    Oct 21, 2019 at 14:16
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    $\begingroup$ @BenBraden Indeed a larger number, I think there are even larger numbers than that! $\endgroup$
    – ThatOneNerdyBoy
    Oct 21, 2019 at 14:17
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    $\begingroup$ 7^77 is bigger, and 7^7^7 way bigger! $\endgroup$
    – wjandrea
    Oct 21, 2019 at 20:56
  • $\begingroup$ Isn't that screenshot from xkcd's "Approximations"? $\endgroup$
    – Cloudy7
    Oct 21, 2019 at 22:14
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Maybe:

${\infty}$

shortest number, that is also the largest

Largest is certainty, shortest for use only 1 character

You can write it with six straight lines, period:

　／＼／＼　　
　＼／＼／, like infinity symbol, and forming a loop(period)　

Update:

Inspired by Trevor Powell, Could be enhanced to:

$11^{111!}$, where equal to $10^{10^{180.263855...}}$ by Wolfram, much larger than $11111!$
(Please accept Trevor Powell's if this is the final answer :P)

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    $\begingroup$ Unfortunately, that is not a number. $\endgroup$
    – Daniel Mathias
    Oct 21, 2019 at 10:04
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    $\begingroup$ perhaps, pedantically, it is not a "number", but it does fit the description of "largest number", which also exists in concept only. $\endgroup$
    – SteveV
    Oct 21, 2019 at 12:20
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    $\begingroup$ It may be a number, but it's not an integer. $\endgroup$
    – Ben Barden
    Oct 21, 2019 at 14:16
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enter image description here Six straight lines and a period. The smallest finite projective plane is the Fano plane PG(2,2) (A projective plane is an ordinary plane equipped with additional "points at infinity".)

If this is too abstract then simply consider

$11^{111!}$

(imagine bars) it is much more than a "googol factorial" although much less than the Graham number. Up arrow notation cannot be used because an arrow contains 3 straight lines and the maximal possible value would be 11

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  • $\begingroup$ hmm... this can be improved with minor adjustment $\endgroup$
    – Daniel Mathias
    Oct 21, 2019 at 15:16
  • $\begingroup$ I know that ! in exponential (as superscript) is even higher, but I don`t know how to type it. I think this is high enough for such an abstract grandpa $\endgroup$
    – balazs.com
    Oct 21, 2019 at 15:19
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    $\begingroup$ See MathJax in edit $\endgroup$
    – Daniel Mathias
    Oct 21, 2019 at 15:39
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    $\begingroup$ In what sense is the Fano plane a number? $\endgroup$
    – Paul Reynolds
    Oct 21, 2019 at 16:36
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    $\begingroup$ Grandpa made the abstraction, I only answered . Grandpa is a bit old but likes weird things: I know his cast of thinking: He always says, Balazs, when you draw a line, it will consist of points of real number of infinite, so the Fano plane is the smallest (in the question phrased as "short") drawing/writing that is also infinite (in the question: "largest") "Number" refers to "number of points" in the answer. Note, that the two "infinites" are not the same, they are also laterally-thought. This is just grandpa....old, but creative. $\endgroup$
    – balazs.com
    Oct 21, 2019 at 17:28
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The answer can be

$2\pi$

written in 6 straight lines like

enter image description here

because

When dealing with angles, $2\pi$ radians ($360^{\circ}$, 1 full revolution) is usually treated as the largest possible angle (due to periodicity - by the way, Grandpa did actually say the word "period" - since any angle outside of $[0; 2\pi)$ interval can be reduced to the one inside it), and "$2\pi$" is the shortest way to write this angle (shorter, than "360 degrees", "400 gons", "1 revolution" etc.)

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  • $\begingroup$ for lateral thinking it`s good:) (However, I would rather write π π to avoid Zπ :P) $\endgroup$
    – balazs.com
    Oct 21, 2019 at 9:55
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    $\begingroup$ @balazs.com Wouldn't it be pi squared rather than two pi? $\endgroup$
    – trolley813
    Oct 21, 2019 at 10:07
  • $\begingroup$ no, this is pi squared ππ (and only five lines in this font type) and this is two pi π π (and there is an interval ("period") between them. Period used twice! $\endgroup$
    – balazs.com
    Oct 21, 2019 at 10:12
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    $\begingroup$ I like the outside-the-box thinking, but grandpa says it's an integer $\endgroup$
    – Matthew Jensen
    Oct 21, 2019 at 20:03
  • $\begingroup$ I now upvoted "us" (collaboration of the pi-s) I think it is a unique answer and satisfies. (Grandpa added his "integer" later in edit) $\endgroup$
    – balazs.com
    Oct 21, 2019 at 20:13
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My answer would be, in words, 11 to the 11th to the 11th, or 11^11^11. Eleven to the eleventh power is 285,311,670,611, and 285,311,670,611 raised to the eleventh is 1.0198e+126 (according to Google).

Update

I've corrected my order of operations. 11^11^11 should yield 3.701 × 10^297121486764 (https://www.wolframalpha.com/input/?i=11%5E11%5E11)

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  • $\begingroup$ You're right! I'd forgotten my order of operations. I've updated my answer. Thanks! $\endgroup$
    – TempleGuard527
    Oct 21, 2019 at 19:18
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I was thinking

1/0

If it's simplified and turned into straight lines it would only require 6. While it is undefined, in a way it's also very large.

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  • $\begingroup$ -1 It is undefined, therefore it can not be very large. $\endgroup$
    – infinitezero
    Oct 21, 2019 at 22:24
  • $\begingroup$ I forgot about the integer part, which this most definitely is not. $\endgroup$
    – AKscout
    Oct 21, 2019 at 22:39

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