# Longest arithmetic expression where the answer is equal to the number of letters [closed]

You can use any mathematical operations represented by English words. These English words must be found in a commonly used dictionary.

Spaces are neither letters nor words.

You can not use the same word twice. No numerical digits are allowed.

Example:

Five plus eight

Is 13, and it has 13 letters.

You objective is to find the longest expression

Inspired by: Find the longest arithmetic expression with value equal to number of letters in its english representation To clarify, the difference here is that you can't repeat a word.

Note: Your full expression must be stated as a whole in your answer. Therefore there's no infinite letter solutions.

• Infinite equals PHP ;) Jun 18 '15 at 18:08
• Please set a standard: Would 21 be hyphenated or not? (I.E., does it count as one word or two?) Jun 18 '15 at 18:15
• Are you allowed to be verbose in the answers? Are you allowed to use an 'equals' to have two sides of the equation equal the same value? Jun 18 '15 at 19:00
• The latest monster uses every number from $0$ to $99$ inclusive. Anything with a higher score must have either: longer names for very large numbers OR more non-number words like the names or constants or more verbose means to say the same thing à la "multiplied with" instead of "times". Jun 19 '15 at 14:14
• I’m voting to close this question because open-ended puzzles are off-topic Aug 15 at 23:19

## 1,720$$\Rightarrow$$4,242$$\Rightarrow$$ 24,749

This can be expanded infinitely so long as we can come up with new names for large numbers. In fact, notice that it starts with a new prefix after $$10^{3,000}$$. You could do the whole list again with the Milli- prefix and then Billi-, Trilli-, etc.

A Million Billion Trillion Quadrillion Quintillion Sextillion Septillion Octillion Nonillion Decillion Undecillion Duodecillion Tredecillion Quattuordecillion Quindecillion Sedecillion Septendecillion Octodecillion Novendecillion Vigintillion Unvigintillion Duovigintillion Tresvigintillion Quattuorvigintillion Quinvigintillion Sesvigintillion Septemvigintillion Octovigintillion Novemvigintillion Trigintillion Untrigintillion Duotrigintillion Trestrigintillion Quattuortrigintillion Quintrigintillion Sestrigintillion Septentrigintillion Octotrigintillion Noventrigintillion Quadragintillion Unquadragintillion Duoquadragintillion Tresquadragintillion Quattuorquadragintillion Quindragintillion Sesquadragintillion Septenquadragintillion Octoquadragintillion Novenquadragintillion Quinquagintillion Unquinquagintillion Duoquinquagintillion Tresquinquagintillion Quattuorquinquagintillion Quinquinquagintillion Sesquinquagintillion Septenquinquagintillion Octoquinquagintillion Novenquinquagintillion Sexagintillion Unsexagintillion Duosexagintillion Tresexagintillion Quattuorsexagintillion Quinsexagintillion Sesexagintillion Septensexagintillion Octosexagintillion Novensexagintillion Septuagintillion Unseptuagintillion Duoseptuagintillion Treseptuagintillion Quattuorseptuagintillion Quinseptuagintillion Seseptuagintillion Septenseptuagintillion Octoseptuagintillion Novenseptuagintillion Octogintillion Unoctogintillion Duooctogintillion Tresoctogintillion Quattuoroctogintillion Quinoctogintillion Sexoctogintillion Septemoctogintillion Octooctogintillion Novemoctogintillion Nonagintillion Unnonagintillion Duononagintillion Trenonagintillion Quattuornonagintillion Quinnonagintillion Senonagintillion Septenonagintillion Octononagintillion Novenonagintillion Centillion Uncentillion Duocentillion Trescentillion Quattuorcentillion Quincentillion Sexcentillion Septencentillion Octocentillion Novencentillion Decicentillion Undecicentillion Duodecicentillion 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Quinquinquagintacentillion Sesquinquagintacentillion Septenquinquagintacentillion Octoquinquagintacentillion Novenquinquagintacentillion Sexagintacentillion Unsexagintacentillion Duosexagintacentillion Tresexagintacentillion Quattuorsexagintacentillion Quinsexagintacentillion Sesexagintacentillion Septensexagintacentillion Octosexagintacentillion Novensexagintacentillion Septuagintacentillion Unseptuagintacentillion Duoseptuagintacentillion Treseptuagintacentillion Quattuorseptuagintacentillion Quinseptuagintacentillion Seseptuagintacentillion Septenseptuagintacentillion Octoseptuagintacentillion Novenseptuagintacentillion Octogintacentillion Unoctogintacentillion Duooctogintacentillion Tresoctogintacentillion Quattuoroctogintacentillion Quinoctogintacentillion Sexoctogintacentillion Septemoctogintacentillion Octooctogintacentillion Novemoctogintacentillion Nonagintacentillion Unnonagintacentillion Duononagintacentillion Trenonagintacentillion Quattuornonagintacentillion Quinnonagintacentillion Senonagintacentillion Septenonagintacentillion Octononagintacentillion Novenonagintacentillion Ducentillion Unducentillion Duoducentillion Treducentillion Quattuorducentillion Quinducentillion Seducentillion Septenducentillion Octoducentillion Novenducentillion Deciducentillion Undeciducentillion Duodeciducentillion Tredeciducentillion Quattuordeciducentillion Quindeciducentillion Sedeciducentillion Septendeciducentillion Octodeciducentillion Novendeciducentillion Vigintiducentillion Unvigintiducentillion Duovigintiducentillion Tresvigintiducentillion Quattuorvigintiducentillion Quinvigintiducentillion Sesvigintiducentillion Septemvigintiducentillion Octovigintiducentillion Novemvigintiducentillion Trigintaducentillion Untrigintaducentillion Duotrigintaducentillion Trestrigintaducentillion Quattuortrigintaducentillion Quintrigintaducentillion Sestrigintaducentillion Septentrigintaducentillion Octotrigintaducentillion Noventrigintaducentillion 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Duononagintatrecentillion Trenonagintatrecentillion Quattuornonagintatrecentillion Quinnonagintatrecentillion Senonagintatrecentillion Septenonagintatrecentillion Octononagintatrecentillion Novenonagintatrecentillion Quadringentillion Unquadringentillion Duoquadringentillion Tresquadringentillion Quattuorquadringentillion Quinquadringentillion Sesquadringentillion Septenquadringentillion Octoquadringentillion Novenquadringentillion Deciquadringentillion Undeciquadringentillion Duodeciquadringentillion Tredeciquadringentillion Quattuordeciquadringentillion Quindeciquadringentillion Sedeciquadringentillion Septendeciquadringentillion Octodeciquadringentillion Novendeciquadringentillion Vigintiquadringentillion Unvigintiquadringentillion Duovigintiquadringentillion Tresvigintiquadringentillion Quattuorvigintiquadringentillion Quinvigintiquadringentillion Sesvigintiquadringentillion Septemvigintiquadringentillion Octovigintiquadringentillion Novemvigintiquadringentillion 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Duononagintaquadringentillion Trenonagintaquadringentillion Quattuornonagintaquadringentillion Quinnonagintaquadringentillion Senonagintaquadringentillion Septenonagintaquadringentillion Octononagintaquadringentillion Novenonagintaquadringentillion Quingentillion Unquingentillion Duoquingentillion Tresquingentillion Quattuorquingentillion Quinquingentillion Sesquingentillion Septenquingentillion Octoquingentillion Novenquingentillion Deciquingentillion Undeciquingentillion Duodeciquingentillion Tredeciquingentillion Quattuordeciquingentillion Quindeciquingentillion Sedeciquingentillion Septendeciquingentillion Octodeciquingentillion Novendeciquingentillion Vigintiquingentillion Unvigintiquingentillion Duovigintiquingentillion Tresvigintiquingentillion Quattuorvigintiquingentillion Quinvigintiquingentillion Sesvigintiquingentillion Septemvigintiquingentillion Octovigintiquingentillion Novemvigintiquingentillion Trigintaquingentillion Untrigintaquingentillion Duotrigintaquingentillion 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Vigintiseptingentillion Unvigintiseptingentillion Duovigintiseptingentillion Tresvigintiseptingentillion Quattuorvigintiseptingentillion Quinvigintiseptingentillion Sesvigintiseptingentillion Septemvigintiseptingentillion Octovigintiseptingentillion Novemvigintiseptingentillion Trigintaseptingentillion Untrigintaseptingentillion Duotrigintaseptingentillion Trestrigintaseptingentillion Quattuortrigintaseptingentillion Quintrigintaseptingentillion Sestrigintaseptingentillion Septentrigintaseptingentillion Octotrigintaseptingentillion Noventrigintaseptingentillion Quadragintaseptingentillion Unquadragintaseptingentillion Duoquadragintaseptingentillion Tresquadragintaseptingentillion Quattuorquadragintaseptingentillion Quinquadragintaseptingentillion Sesquadragintaseptingentillion Septenquadragintaseptingentillion Octoquadragintaseptingentillion Novenquadragintaseptingentillion Quinquagintaseptingentillion Unquinquagintaseptingentillion Duoquinquagintaseptingentillion 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Quattuorvigintioctingentillion Quinvigintioctingentillion Sesvigintioctingentillion Septemvigintioctingentillion Octovigintioctingentillion Novemvigintioctingentillion Trigintaoctingentillion Untrigintaoctingentillion Duotrigintaoctingentillion Trestrigintaoctingentillion Quattuortrigintaoctingentillion Quintrigintaoctingentillion Sestrigintaoctingentillion Septentrigintaoctingentillion Octotrigintaoctingentillion Noventrigintaoctingentillion Quadragintaoctingentillion Unquadragintaoctingentillion Duoquadragintaoctingentillion Tresquadragintaoctingentillion Quattuorquadragintaoctingentillion Quinquadragintaoctingentillion Sesquadragintaoctingentillion Septenquadragintaoctingentillion Octoquadragintaoctingentillion Novenquadragintaoctingentillion Quinquagintaoctingentillion Unquinquagintaoctingentillion Duoquinquagintaoctingentillion Tresquinquagintaoctingentillion Quattuorquinquagintaoctingentillion Quinquinquagintaoctingentillion Sesquinquagintaoctingentillion 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Nonagintaoctingentillion Unnonagintaoctingentillion Duononagintaoctingentillion Trenonagintaoctingentillion Quattuornonagintaoctingentillion Quinnonagintaoctingentillion Senonagintaoctingentillion Septenonagintaoctingentillion Octononagintaoctingentillion Novenonagintaoctingentillion Nongentillion Unnongentillion Duonongentillion Trenongentillion Quattuornongentillion Quinnongentillion Senongentillion Septenongentillion Octonongentillion Novenongentillion Decinongentillion Undecinongentillion Duodecinongentillion Tredecinongentillion Quattuordecinongentillion Quindecinongentillion Sedecinongentillion Septendecinongentillion Octodecinongentillion Novendecinongentillion Vigintinongentillion Unvigintinongentillion Duovigintinongentillion Tresvigintinongentillion Quattuorvigintinongentillion Quinvigintinongentillion Sesvigintinongentillion Septemvigintinongentillion Octovigintinongentillion Novemvigintinongentillion Trigintanongentillion Untrigintanongentillion Duotrigintanongentillion Trestrigintanongentillion Quattuortrigintanongentillion Quintrigintanongentillion Sestrigintanongentillion Septentrigintanongentillion Octotrigintanongentillion Noventrigintanongentillion Quadragintanongentillion Unquadragintanongentillion Duoquadragintanongentillion Tresquadragintanongentillion Quattuorquadragintanongentillion Quinquadragintanongentillion Sesquadragintanongentillion Septenquadragintanongentillion Octoquadragintanongentillion Novenquadragintanongentillion Quinquagintanongentillion Unquinquagintanongentillion Duoquinquagintanongentillion Tresquinquagintanongentillion Quattuorquinquagintanongentillion Quinquinquagintanongentillion Sesquinquagintanongentillion Septenquinquagintanongentillion Octoquinquagintanongentillion Novenquinquagintanongentillion Sexagintanongentillion Unsexagintanongentillion Duosexagintanongentillion Tresexagintanongentillion Quattuorsexagintanongentillion Quinsexagintanongentillion Sesexagintanongentillion Septensexagintanongentillion Octosexagintanongentillion Novensexagintanongentillion Septuagintanongentillion Unseptuagintanongentillion Duoseptuagintanongentillion Treseptuagintanongentillion Quattuorseptuagintanongentillion Quinseptuagintanongentillion Seseptuagintanongentillion Septenseptuagintanongentillion Octoseptuagintanongentillion Novenseptuagintanongentillion Octogintanongentillion Unoctogintanongentillion Duooctogintanongentillion Tresoctogintanongentillion Quattuoroctogintanongentillion Quinoctogintanongentillion Sexoctogintanongentillion Septemoctogintanongentillion Octooctogintanongentillion Novemoctogintanongentillion Nonagintanongentillion Unnonagintanongentillion Duononagintanongentillion Trenonagintanongentillion Quattuornonagintanongentillion Quinnonagintanongentillion Senonagintanongentillion Septenonagintanongentillion Octononagintanongentillion Novenonagintanongentillion Millinillion Millimillion Millibillion Millitrillionths multiplied with the value of e raised to i times pi plus Legendre's Constant minus negative Twenty-four Thousand Seven Hundred Forty Nine


In numerical form, it can be expressed as:

$$\prod_{n=1}^{1,003}10^{3n}\div10^{3,012}*(e^{i\pi}+1)+24,749$$

Legendre's Constant

• You could just cram in more numeric words by replacing the first bit with sum of ... times 0 .... Sum is an arithmetic operation, and lets you list nearly arbitrary numbers. Such as sum of two halves, three thirds, four quarters, five fifths, six sixths, seven sevenths, etc... Jun 19 '15 at 6:57
• Would words like fifty-six, eighty-three etc be found in a commonly used dictionary?
– user5971
Jun 19 '15 at 7:00
• if you REALLY wanna max it out, use this site and pick the longest words from there. I am too lazy, and I am busy at work.
– JLee
Jun 19 '15 at 11:57
• @Evert Do you accept Dictionary.com? It's my most commonly used dictionary. Fifty-six and eighty-three both have entries. Jun 19 '15 at 12:14
• @JLee I actually had the word "One" in there twice, too. I've triple-checked this latest entry. Feel free to check behind me as I have obviously created errors in the past. Jun 19 '15 at 14:11

## 624

Before you read the huge number below, realize my strategy: I am creating a number so huge that it cannot be written out, BUT, at the end it is multiplied by zero, and then 624 is added.

I am sure that someone could use this same strategy to get a much larger (longer) number than this.

Also note that the numbers twenty-one through ninety-nine are hyphenated, making each of them one word. Thus, the word twenty is not in the word twenty-one, and so on.

Absolute value of ninety-nine centillion ninety-eight vigintillion ninety-seven novemdecillion ninety-six octodecillion ninety-five septendecillion ninety-four sexdecillion ninety-three quindecillion ninety-two quattuordecillion ninety-one tredecillion ninety duodecillion eighty-nine undecillion eighty-eight decillion eighty-seven nonillion eighty-six octillion eighty-five septillion eighty-four sextillion eighty-three quintillion eighty-two quadrillion eighty-one trillion eighty billion seventy-nine million seventy-eight thousand multiplied by seventy-seven googol to the seventy-six googolplex power minus seventy-five over seventy-four score times zero plus six hundred twenty-four

• Nice one :) (Now who wants to check his work to make sure the characters are the right length lol) Jun 18 '15 at 22:58
• I used a formula in Excel to calculate the length minus the spaces: =LEN(SUBSTITUTE(A2," ","")). Otherwise it wouldn't have been fun!
– JLee
Jun 18 '15 at 23:29

## 145 Points

$$\lvert\frac{\sqrt{9^2}}{\frac{1}{8^3}}\rvert+11+(e^{i\pi}*\frac{18,000}{10})-\frac{2,674,000}{1,000}$$

In English, this can be described as:

Absolute value of root nine squared divided by inverse eight cubed plus eleven and $$e$$ to $$i$$ $$pi$$ times eighteen thousand tenths minus two point six seven four million thousandths.

Without spaces, that transcription is 145 characters. Mathematically, it evaluates in the following manner:

$$\lvert\frac{\sqrt{81}}{\frac{1}{512}}\rvert+11+(-1*1,800)-2,674$$

$$\lvert9*512\rvert+11-1,800-2,674$$

$$\lvert4,608\rvert-4,463=4,608-4,463=145$$

• Wow......I give up (bows down) Jun 18 '15 at 19:18
• "two point six seven four million thousandths"? I'm glad I never had you as a math teacher... Jun 18 '15 at 19:35
• Jeez... I wanna know how you come up with this stuff! Jun 18 '15 at 19:42
• You can stretch this a little further. Replace "eleven" with "one hundred forty three billion billionths" and "eighteen thousand tenths" with "nineteen thousand tenths" Jun 18 '15 at 19:42
• using and for plus? it's not the same thing though
– JLee
Jun 18 '15 at 19:56

95 Points

square root of a hundred times four plus eleven minus one multiplied by two where ten is substracted and five added (95 letters)

which value is:

$\sqrt{100} \times 4 + 11 - 1 \times 2 - 10 + 5 = 95$

67 points

My attempt:

two squared, to the power of five, multiplied by itself, plus eight, minus sixty-nine

which value is:

$((2^2)^5)^2 + 8 - 69 = 67$

It's actually infinite. you can keep going forever using subtraction, here's an example.

one billion minus nine hundred ninety-nine million, nine hundred ninety-nine thousand, nine hundred.
^- equals 100, and has one hundred characters.

onehundredminusseventyfour is 26 characters and evaluates to 26. It wouldn't be hard to go beyond that.
onethousandminusninehundredsixtyfour is 36
Just for fun: thisstatementevaluatestothenumberonehundredfiveplusfortyexponentzero

105 + 40^0 = 106.

Come to think of it, this contest is going to end in an arbitrarily large number as the winning entry just because someone's going to figure out how to create a word problem with no repeating word, and then it's going to be a hassle reading through it to verify that it doesn't have any spelling, grammar, or punctuation errors while still using exactly one of each English word (which, I might add, is a constantly expanding language.)

with spaces: in wabambuule, mystical land o' honeycombs and rabbits, a tribe of pixies lives. They require thirty one trombones. sprites from the neighboring borough need two hundred three. how many total musical instruments are needed? give your answer to nearest hundredth decimal place

a few notes:
1. Yes, I made up a name but any word will fit there.
2. There are still quite a few synonyms for fairies I can use to expand this.
3. I have any number of musical instruments to add.

You could also just say --------...---infinity, where you have an infinite number of negation operators (which don't count as a repeated word, and are not expressly forbidden, and are not expressly stated not to count), but I'm going to assume that's out of the bounds of the problem because the whole point was to remove some of the loopholes that made the original problem go infinite.

• You can not use the same word twice Jun 18 '15 at 18:28
• whoops! Guess I'll use this as a starting point then. If spaces don't count, what about commas? They're grammatically important. Jun 18 '15 at 18:29
• Your example for 106 only has 68 characters in it. Have I missed something? Jun 18 '15 at 19:16
• Sorry about that, I was using Notepad++ to count the number of characters and forgot to delete the previous example. Jun 18 '15 at 19:31
• In your latest edit, you use "of" twice... Jun 18 '15 at 19:41

$\Large\infty {\rm\ Points}$

If acronyms are allowed, one could technically construct the infinite-point acronym "an AAPO plus one", where AAPO is a recursive acronym that stands for "an AAPO plus one".

I believe, given a sufficiently large team of lawyers, this could be proven to not violate the prohibition on repeated words nor the prohibition on using words not in the English language.

• Y'know great questions often get ruined and labeled "Too broad" when people find loopholes such as these. I'm editing the question... Jun 19 '15 at 23:26
• It's a gag answer anyway. ;)
– COTO
Jun 20 '15 at 0:49