6
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This is a multilingual generalized follow-on to "What number is that? Asks Grandpa", which I restate as:

"What is the smallest positive English integer N, for which if you take its WORD anagram and subtract the number N itself, you get some positive integer quantity:

Anagram of the number - number > zero

  • Hence the smallest legal number in English would be 76 (SEVENTY-SIX), since 67 (SIXTY-SEVEN) is also a legal number, and 76 - 67 is positive. (Doesn't work for TWENTY, THIRTY, FORTY, FIFTY since their tens-multiple is spelled differently to their units number. And of course teens are irregular in most languages).
  • No archaic spellings, e.g. 'FOURTY' is not allowed.
  • In order to keep this objective we probably have to exclude numerical terms like 'OVER-FIFTY', 'DUO', 'DECADE', 'DOZEN', 'CENTURY', 'MYRIAD' etc., let alone subjective/cryptic ones like 'SENIOR' = OVER-FIFTY-FIVE, 'TEENAGER' = $<$your choice of number between 13..19$>$
  • and ZERO/NULL/NUL/NOTHING/NIX/... probably has a very high number of subjective/cryptic synonyms.
  • Ignoring hyphens
  • Either ignoring accents, or optionally using their accepted ASCII transliterations, e.g. 'ä' -> AE,'ø' -> OE, 'ß' -> SS

So what's the smallest such positive integer in French? German? Spanish? Italian? Dutch? Swedish? Esperanto? etc.

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  • $\begingroup$ No-computers suggested, but I think this is a more interestiing non-trivial '99 Bottles of Beer' challenge if you do do it by computer. $\endgroup$ – smci May 14 at 18:09
  • 1
    $\begingroup$ Interestingly, you can find the non-trivial rearrangements in many languages here. $\endgroup$ – El-Guest May 14 at 18:30
  • 1
    $\begingroup$ Isn't the $>0$ condition irrelevant? Since if $x-y<0$ then $y-x>0$. So really isn't this puzzle just "What is the smallest number that has an anagram that is also a number"? $\endgroup$ – BioPhysicist May 15 at 14:11
  • $\begingroup$ @AaronStevens, I suppose, but I wanted to keep the phrasing of the 'Ask Grandpa' original, so that English answers would be portable. $\endgroup$ – smci May 15 at 14:29
  • $\begingroup$ True. And I guess it is a little different now that I think about it. The question is "what is the smallest number that has an anagram that is a number smaller than itself" $\endgroup$ – BioPhysicist May 15 at 14:32
11
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In Mandarin Chinese:

十二 and 二十

Am I cheating?

Actually no! In Latin Pinyin
Twelve is 十二, Shí èr
Twenty is 二十, Èr shí

Note: this is also valid for Japanese as they share the same numerals!

In Braille:

12 ⠼⠁⠃
21 ⠼⠃⠁

In Arabic:

34 أربعة و ثلاثون
43 ثلاثة و أربعون

In Sino-Korean Cardinal Numerals written in Hangul:

12 십이
21 이십

In Morse Code:

1 ---.
9 .---
And we might have reach here a minimum!

In Roman Numerals:

4 IV
6 VI
Note that this is using a numeral system and not a language unlike previous examples. This is a numerals anagram instead of a words anagram. Thanks to @El-Guest for pointing this out. If those are allowed, you could have:
Binary
5 $\implies$ 101
6 $\implies$ 110
And create plenty with here.

For Binaries if...

... We write it in English, but that's not a justified choice, apart because we are in an English website, then:
$12\implies 1~100\implies$ one thousand one hundred
$40\implies 101~000\implies$ one hundred one thousand

Note for Latin:

I have tested all pairs within $1$ to $100$ without finding an anagram. I am currently looking for a longer list. I have ask StackExchange Latin community. You can help answer if you have one!

Note for Hindi, maybe this is gonna help someone on this one:

I have tested all pairs from 1 to 100 without finding an anagram. Like for Latin language, my list is too short. And it seems there isn't a StackExchange site where I can ask if someone has a longer one! I'm sharing mine to you:
["शून्य","एक","दो","तीन","चार","पांच","छह","सात","आठ", 10:"नौ", "दस","ग्यारह","बारह","तेरह","चौदह","पंद्रह","सोलह","सत्रह","अठारह","उन्नीस", 20:"बीस","इकीस","बाईस","तेइस","चौबीस","पच्चीस","छब्बीस","सताइस","अट्ठाइस","उनतीस", 30:"तीस","इकतीस","बतीस","तैंतीस","चौंतीस","पैंतीस","छतीस","सैंतीस","अड़तीस","उनतालीस",40:"चालीस","इकतालीस","बयालीस","तैतालीस","चवालीस","पैंतालीस","छयालिस","सैंतालीस","अड़तालीस","उनचास", 50:"पचास","इक्यावन","बावन","तिरपन","चौवन","पचपन","छप्पन","सतावन","अठावन","उनसठ", 60:"साठ","इकसठ","बासठ","तिरसठ","चौंसठ","पैंसठ","छियासठ","सड़सठ","अड़सठ","उनहतर", 70:"सत्तर","इकहतर","बहतर","तिहतर","चौहतर","पचहतर","छिहतर","सतहतर","अठहतर","उन्नासी", 80:"अस्सी","इक्यासी","बयासी","तिरासी","चौरासी","पचासी","छियासी","सतासी","अट्ठासी","नवासी",90:"नब्बे","इक्यानवे","बानवे","तिरानवे","चौरानवे","पचानवे","छियानवे","सतानवे","अट्ठानवे","निन्यानवे", 100:"एकसौ"]

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  • 1
    $\begingroup$ The same goes for 十二 (twelve, shí èr) and 二十 (twenty, èr shí) as well. $\endgroup$ – Toby Mak May 15 at 1:22
  • $\begingroup$ @TobyMak, thanks! I don't know how I could miss that. $\endgroup$ – JKHA May 15 at 2:08
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    $\begingroup$ This is ridiculously random. Had to upvote. $\endgroup$ – merrybot May 15 at 4:16
  • $\begingroup$ In Roman Numerals, it would be 6 (IV <=> VI). $\endgroup$ – Ramillies May 15 at 17:55
  • 2
    $\begingroup$ Roman numerals shouldn’t count — however if you find a Latin pair it would. 4 and 6 are quattuor and sex, respectively and so don’t represent word anagrams (only numeral anagrams). (Similar with binary) $\endgroup$ – El-Guest May 16 at 20:09
6
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I wasn't sure whether hyphens counted.

Croatian:

Dvadeset tisuća (20000) turns into dvije tisuće deset (2010)

Dutch:

Veertienmiljard eenentwintigmiljoen driehonderdduizend (14021300000) turns into een miljard dertien miljoen twintig­duizend­vier­honderd­een (1013020401)

Esperanto:

Dudek mil (20000) turns into du mil dek (2010)

Estonian:

Kaheksakümmend üks (81) turns into kakskümmend (20)

French:

Deux cent vingt-quatre (224) turns into cent quatre-vingt-deux (182)

Hungarian:

Két­ezer­öt­száz­negyven­öt (2545) turns into ezer­négy­száz­ötven­kettő (1452)

Italian:

Tredici milioni sedici­mila­otto­cento­trenta­sette (13016837) turns into Dieci milioni diciassette­mila­tre­cento­trent­otto (10017338)

Norwegian:

Femti tusen (50000) turns into fem tusen ti (5010)

Portuguese:

Dez milhões e noventa e oito mil turns into nove milhões e doze mil e oitenta

Spanish:

Trece millones ciento setenta y seis mil seiscientos (13176600) turns into cinco millones siete mil trescientos sesenta y siete (5007367)

Swedish:

Femton miljoner trettio­tusen ett­hundra (15030100) turns into tio miljoner tretton­tusen fem­hundra­ett

These were sourced from this website.

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  • 2
    $\begingroup$ I doubt that any of these are actually the smallest such number for the language in question? $\endgroup$ – jafe May 14 at 19:57
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    $\begingroup$ @jafe and smci, on the website it's written : here are the smallest known non-trivial number anagrams in various languages $\endgroup$ – JKHA May 14 at 23:33
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    $\begingroup$ For example, in French: QUATRE-VINGT (80), VINGT-QUATRE (24) is obviously smaller. Is it the smallest? $\endgroup$ – smci May 15 at 5:11
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    $\begingroup$ @smci, we do write QUATRE-VINGTS from my old memories ^^ $\endgroup$ – JKHA May 15 at 5:25
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    $\begingroup$ I do not see how those Croatian numbers are anagrams of each other: one has a 'j' the other not ? $\endgroup$ – daw May 15 at 13:19
6
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In Dutch:

vijfenzestig (65) - zesenvijftig (56) = 9 > 0

Not sure why William found such a large number. We're only a small country after all ...

In German:

vierundfünfzig (54) - fünfundvierzig (45) = 9 > 0

In Russian:

тридцать два (32) - двадцать три (23) = 9 > 0

In French (only slightly smaller than William's entry, and it's not a digit anagram):

deux cent vingt (220) - cent vingt-deux (122) = 98 > 0

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    $\begingroup$ Yes :D I don't speak Dutch at all and as I say, it was just from the Math Magic website that El-Guest mentioned $\endgroup$ – William Pennanti May 14 at 19:19
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    $\begingroup$ Ah, those are the smallest non-trivial ones. These are pretty trivial, I admit ... $\endgroup$ – Glorfindel May 14 at 19:19
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    $\begingroup$ Yours are word anagrams but the numbers themselves aren't (e.g. Croatian - 20000 has different digits than 2010). $\endgroup$ – Glorfindel May 14 at 19:25
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    $\begingroup$ Ahh, ok. I didn't realise that was the challenge. $\endgroup$ – William Pennanti May 14 at 19:26
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    $\begingroup$ @TobyMak yes, the rules are clear and they don't have to be number anagrams. However, those are solutions which are tend to be (much) smaller, which is the aim of the question. $\endgroup$ – Glorfindel May 15 at 5:51
3
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Turkish

Üç yüz iki (302) - iki yüz üç (203) > 0

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  • $\begingroup$ It that really the smallest in Turkish? Can you add explanation for non-Turkish speakers why smaller multiples of tens and hundres won't work? $\endgroup$ – smci May 16 at 17:14
  • $\begingroup$ For numbers that are multiple of ten up to 100 are like this 10 (on) 20 (yirmi) 30 (otuz) 40 (kırk) 50 (elli) 60 (altmış) 70 (yetmiş) 80 (seksen) 90 (doksan). I could not find anagrams. $\endgroup$ – Orçun Çolak May 16 at 17:42
  • $\begingroup$ I mean you might like to edit your answer to show the Turkish words for 20, 30, 200, 300 etc. to illustrate why they don't work. $\endgroup$ – smci May 16 at 17:46
  • $\begingroup$ In the range of 100-200 I couldn't find any. 100(yüz) 102 (yüz iki). Anagram of 102 is iki yüz (200) but it is not smaller. Multiples of tens in 100 range also have no anagrams. $\endgroup$ – Orçun Çolak May 16 at 17:56
  • 1
    $\begingroup$ In the range of 200-300 201( iki yüz bir) Could have anagram bir yüz iki (102) but it is not grammatical. In the range of 300-400 302 (üç yüz iki) has anagram iki yüz üç (203). So this is smaller than my original answer. Thank you for making me find a better answer :) $\endgroup$ – Orçun Çolak May 16 at 18:02
2
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Norwegian has the trivial

SEKSTIFEM - FEMTISEKS (65-56=9)

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1
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In Laádan, a constructed language:

thab (10) turns into bath (6) and 10 - 6 > 0

The source for these words is here. Laádan is a feminist constructed language which was used in the science fiction series Native Tongue (Wikipedia).

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  • $\begingroup$ You mean 6, bath! $\endgroup$ – JKHA May 15 at 2:56
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    $\begingroup$ Thanks, it's now corrected. $\endgroup$ – Toby Mak May 15 at 2:57
1
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As in other languages, the least in Hebrew is

34, שלושים וארבע, anagramming to ארבעים ושלוש, 43. Numbers in the teens and twenties don't use the words, respectively, for "one" and "two".

In traditional Hebrew numerals (still used today for some purposes), the least is

11, י״א, anagramming to א׳י׳, 1010. Anything smaller is one letter.

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1
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In Czech:

32 (třicet dva) - 23 (dvacet tři) = 9

In Polish:

65 (Sześćdziesiąt pięć) - 56 (Pięćdziesiąt sześć) = 9

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0
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In German, I'm pretty sure the answer is:

54: VIERUNDFÜNFZIG anagrams to FÜNFUNDVIERZIG=45 Cannot use anything in the 20s since 2 is zwei but 20 is zwanzig, or the 30s since 30 is dreißig, not dreizig.

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    $\begingroup$ Didn't see Glorfindel's above...apologies. $\endgroup$ – Jeremy Dover May 14 at 19:20

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