Past problems

Test problems from past UKLO competitions



Below you will find a list of all the test problems that have been used in UK Olympiads since 2010. Each problem includes a link to the downloadable problem.  (To see the link, move the bar beneath the table to the right.)

Each problem is listed with the following information in columns (revealed by scrolling the bar beneath the table):

  • diff: its relative difficulty, as explained below
    • (Note: for problems set in 2010 and 2011 we have to rely on an informal grading in the two books of problems. This five-point grading is partly based on test scores in the American competition and partly estimated by test-setters; unfortunately there are no problems graded by both systems, so they are hard to match. The Japanese problem from 2011 isn’t included in these books so its grading is just a guess.)
  • year: the year in which it was used in UKLO
  • number, name: its number in that year’s problem set, and its name
  • language: the language(s) from which its data are taken
  • ‘area’: what area of linguistics does it involve – script, number-systems, change, morphology, etc. The classification is regrettably crude and inconsistent, but it is indicative.
  • download: a hyperlink to the URL of a file containing the problem concerned, together with any extra material.
  • author: the name of the person or people who wrote the problem.

The problems

The problems are listed in the table below. Note that:

  • all the problems are stored on the UKLO website, and you can download them by clicking in the ‘download’ column (which may be hiding on the right – just slide the bar at the foot of the table).
  • the table is divided into a number of pages which you can step through by pressing the button on the bottom right, but you can also choose how many rows to display in each page, for a number between 10 and 100.
  • in spite of this division into pages, you can reorder the rows by clicking on the column headers; e.g. instead of the default ordering by year you can order by difficulty, starting either with the easiest or the hardest.
  • there’s a useful search box in the top right of the table, so (for instance) you can search for all the problems based on English by typing “English” into that box.
  • to see all the columns, you need to scroll horizontally using the bar at the foot of the table. The columns on the right include ‘download’ and ‘author’. Depending on your browser, you may find that the number of visible columns depends on the number of rows displayed, but you may be able to view more columns by refreshing your page.
  • each problem includes its solution, but most of them also have some kind of commentary. Those that have NO commentary are marked with *.


The table of problems

[Table displayed with Tablepress – highly recommended!]
diffyearnumber, namelanguageareadownloadauthor
12010*1. Sorry we have no red cucumbersFrenchsyntax Radev
120102. Gelda’s House of GelbergargEnglishgeneral Schneider
12010*3. Say it in AbmaAbmageneral Kedova & Rachel Nordlinger
12010*R2.3. F u cn rd thsEnglishcomputing Sproat
22010*R2.1. Ardhay UzzlepayMinangkabaugeneral Henderson
32010*4. Lost in YerevanArmenianscript Radev
32010*7. Texting, texting, one two threeEnglishcode Littell
32010*R2.2. Be Cree-ativeCreescript Littell & Julia Workman
32010*6. Tangkhul tangleTangkhulgeneral Mortensen
32010*R2.4. Tale of KieuVietnamesescript Mortensen
32010*R2.5. Possessed in VanuatuVanuatugeneral Simpson & Jeremy Hammond
52010*5. Turkish delightTurkishgeneral Bozhanov
0.520112. JapaneasyJapanesescript Somers
22011*7. The war of the dotsEnglish (braille)script Littell
22011*R2.1. Stopping and flapping in WarlpiriWarlpirigeneral Laughren
22011R2.2. Counting in IrishIrishnumber Payne
22011*1. Running on MTEnglishmeaning Somers
220113. Doubling in Caterpillar CountryArrerntegeneral Dras & Mary Laughren
22011*5. Mix up on the farmPapagogeneral Levin (data from Ken Hale)
22011*6. Tiger taleIndonesiangeneral Radev
320114. Ulwa possessivesUlwageneral Sproat
42011*R2.5. Swallow the saltTadaksahakgeneral Bozhanov
52011*R2.3. Axolotl in the waterNahuatlgeneral Berman
52011*R2.3. A script for the NdyukaNdyukascript Littell
0.8920121. Being with it in YolmoYolmogeneral Gawne
0.9220122. Danish numbersDanishnumbers Swan
1.172012*6. Crocodile BardiBardigeneral Sheard
1.3620123w. Welsh librariesWelshgeneral Hudson
1.592012*8. Arcturan intergalactic peace messagefictitious languagegeneral Zwarts
1.692012*7. Waorani numbersWaoraninumbers Radev
1.722012*R2.2. Who is good?Luiseñogeneral Langacker (via Dick Hudson)
1.7620124. HaitianHaitiangeneral Youmerski
1.932012*5. EsperantoEsperantogeneral Pegushev
2.222012*R2.1. A fox among the hEnglishcomputing Littell
2.352012*R2.3. The little engine that could… readEnglishlogic Pustejovsky, Patrick Littell
2.42012*9. WaanyiWaanyigeneral Laughren
3.062012R2.5. Catalan pluralsCatalanmorphophonology Iomdin
3.3920123d. Dutch past participlesDutchgeneral Newsome
33.332012*R2.4. 100 surnamesPhags-pascript Littell
1.22013*8. A little Dutch problemDutchgeneral Somers
1.442013*5. BulgarianBulgariansyntax Bozhanov
1.562013*1. YodaspeakEnglishsyntax Somers
1.7920136. The long and short of English verbsEnglishgeneral Hudson
2.122013*3. PaliPaligeneral Newsome
3.2920139. BengaliBengaligeneral Bozhanov
3.4920134a. Arabic scriptArabicscript Palfreyman
5.632013*R2.4. Stockholms TunnelbanaSwedishgeneral Littell
5.742013*R2.1. Deer FatherQuechuageneral Littell
6.0620134s. The Shavian AlphabetEnglish – Shavianscript Newsome
8.722013*7. PhoenicianPhoenicianscript Somers
9.992013*R2.5. Playing the cognate gameIndonesian, Swahilietymology Sheard
12.672013*R2.3. BejaBejageneral Hudson
32.942013*R2.2. Putting the books in orderGeorgian, Armenianscript Radev
0.5420143. MokileseMokilesegeneral Siegel
0.6720141. What time is it in Tallinn?Estoniangeneral Newsome
1.0820142. Maori loanwordsMaorigeneral Littell
1.2620146. Kairak verbsKairakgeneral Schneider
1.3820144. Running speechEnglishphonetics, script Barry & Dick Hudson
2.9920145. TurkishTurkishgeneral Palfreyman
3.2420147. IlokanoIlokanogeneral Bozhanov
3.9820149. LontaraBuginesescript Voss
4.612014*R2.1. Kiswahili verbsKiswahiligeneral
6.482014*R2.2. Untangling TanghulicKachai, Tusom, Ukhrulcomparison Mortensen
6.682014*R2.4. Navajo gophersNavajogeneral Newsome
8.112014*R2.3. Learning YidinyYidinygeneral Laughren
9.012014*R2.5. Hungarians in a fieldHungarianpuzzle Hesterberg
16.9920148. Musical codeEnglishcode Somers
1.062015*1. Counting in KarelianKareliannumbers Trousdale
1.262015*2. Georgian placesGeorgianscript Rucki
1.322015*3. Polish your PolishPolishgeneral Rucki
1.512015*4. Old EnglishEnglishgeneral Trousdale
1.592015*5. Elder FutharkNorsescript Sheard
1.762015*8. Can you finish Finnish?Finnishgeneral Newsome
2.132015*7. MurrinhpathaMurrinhpathageneral Nordlinger
2.462015R2.3 Do-this-do-thatHmonggeneral Mortensen
2.562015*9. Zoink!Englishsemantics Radev with Christiane Fellbaum and Jonathan May
2.742015*6. Japanese placesJapanesegeneral Somers
3.632015R2.2 Malagasy crossnumberMalagasynumbers McCoy
6.52015*R2.4 AymaraAymaraphonology Falk
8.5820155 RomanceLatin, French, Catalan, Romanianhistorical comparison Palfreyman
9.432015*R2.1 MaxakaliMaxakaligeneral Wade
9.48201510. Georgian EraGeorgianscript, general Demszky
0.920162. ForeignFrench, German, Spanishcomparative Hudson
0.920164. Beijing subwayChinesescript Sheard
120161. AlphabetGreekscript Hudson
1.320169. NhandaNhandageneral Verhoeven
1.320168. SomaliSomalimorphology Somers
1.420166. KaqchikelKaqchikelgeneral Yoshitaka Erlewine
1.420163. WatsoniumIrishspelling of loans D’Altuin and Harold Somers
1.420165. AmeleAmelegeneral Verhoeven
1.52016R2.1 MalayMalaygeneral Bozhanov
1.620167. The strange case of the Estonian languageEstoniangeneral Venkataramana
1.82016R2.2. TocharianTocharianhistorical Sayeed
2.12016R2.5. Get edumacated!Englishphonology Littell
2.2201610. Don't sell the house!Nunggeneral Wade
2.82016R2.4. DevanagariDevanagariscript Gawne
2.82016R2.3. HuliHulinumbers Huang
0.92017R1.3. We are all European9 languagescomparative Newsome
1.052017R1.1. Our Italian familyItalianmorphosyntax Hudson
1.182017R1.5. Basquing in the sunBasquemorphosyntax Blackwell
1.392017R1.4. A little TshilubaTshilubamorphosyntax McCoy
1.422017R1.2. Inuktitut scriptInuktitutscript Sayeed
1.772017R1.6. Maori for the beachMaorigrammar Blackwell
1.772017R1.8. ChoctawChoctawmorphosyntax Newsome
2.652017R1.9. The goat, the mother and the Abkhaz wardrobeAbkhazgrammar Andersson, Oliver Sayeed, and Elysia Warner
2.842017R2.1. NepaliNepaligrammar Newsome
2.882017R2.3. VietVietnamesegrammar Hyett
3.22017R1.10. Kaytetye kinshipKaytetyesemantics Turpin
3.322017R2.2. Do you see what I see?Proto-Algonquianmorphosyntax Lovsted
4.022017R2.4. Muddled hieroglyphsEgyptianscript Hudson
4.232017R1.7. On the right Tamil trackTamilscript Low
4.352017R2.5. Magic Yup’ikYup'iknumber Low
0.71201818.1 (In)definitely RomanianRomaniangeneral Barron
0.81201818.2 Lithuanian road tripLithuaniangeneral Newsome
1.19201818.5 At Ease in GilberteseGilbertesegeneral Salter
1.28201818.3 Finding your way in SofiaBulgarianscript Newsome
1.95201818.6 Are you OK with N’ko?Nkoscript Newsome, Harold Somers
1.96201818.4 What's yours is mine (for eating)Fijiangeneral Papp
2.7201818.7 Icelandic RelationsIcelandicgeneral Newsome
4.64201818.R2.4 It’s true: The truth about Chalcatongo MixtecMixtecgeneral Newsome
5.07201818.R2.2 NivkhNivkhgeneral Newell
5.3201818.R2.3 MenyaMenyageneral Blackwell
5.93201818.8 Vietnamese MatchingVietnamesegeneral McCoy, Pat Littell, and Lori Levin
6.1201818.10 Tirana touristAlbaniangeneral Sharman
15.26201818.9 Central Pamerican sumsPamenumber Veneva
0.842019P2 JapaneseJapanesescript Newsome
1.022019P3 JahaiJahaimeaning Newsome
1.312019P4 WelshWelshmorphosyntax Newsome
1.352019P5 PitjantjatjaraPitjantjatjarageneral Dafina and Wilmoth
1.492019P1 LadinLadingeneral Barron
1.822019P7 HarmongolianMongolianmorphophonology Chi
2.042019P9 NdebeleNdebelegeneral Salter
2.642019R2.2 LepchaLepchascript Chi
2.942019P10 BrailleEnglishscript Newsome
3.012019R2.1 AfrihiliAfrihiligeneral Salter
3.642019P6 Cippus AbellanusOscanscript Salter
3.982019R2.4 CupenoCupenogeneral Lovsted
4.682019R2.5 Witsuwit'enWitsuwit'engeneral Lovsted, Sam Ahmed, Ellie Warner
4.852019R2.3 PolishPolishmorphophonology Veneva
17.582019P8 GumatjGumatjnumbers Chi
0.9220201.02 Curious cuneiformBabylonianscript Worthington
1.0120201.05 Hello Mongo!Lomongomorphophonology Liang
1.0620201.03 Norwedish?Norwegian, Swedishcomparative
1.1320201.01 DutchDutchmorphophonology McKnight
1.820201.09 Can Yukaghir?Kolyma Yukaghirgeneral Tsuyoshi
1.8520201.04 The long and short of LigurianLigurianphonology Liang
2.1720201.08 Stressed out in the CaribbeanPapiamentuphonology Sommers
2.4420201.07 A Cat in a HatChintanggeneral Blackwell
320202.1 Taiwan PaiwanPaiwansyntax Ahmed
3.0120202.4 Imitating UteUtesyntax McKnight
3.4520202.5 Arapaho morphologyArapahomorphology Lovsted
3.5220202.2 Yoruba numbersYorubacounting system Somers
3.8120202.3 A toad's miaoMiaoscript Chi
4.320201.10 IñapariIñaparigeneral Ahmed
7.3420201.06 Idalion tabletGreekscript Salter
0.8920211. OghamGaelicscript Verhoeven
0.9120213. WaamaWaamageneral Blackwell
0.9720212. KabyleKabylemorphosyntax Sato, Simi Hellsten
1.522021A2. Old ChineseOld Chinesephonological change Chi
1.720214. Ditema tsa DinokoDitemascript Salter
1.9620217. LatvianLatvianwhole-text translation Blackwell
2.1920215. FilipinoFilipinosyntax, pragmatics Verhoeven
2.3320216. LongguLonggusemantics Verhoeven
2.832021A3. NgkolmpuNgkolmpunumbers Hellsten
3.072021A1. MandombeMandombescript Chi
3.222021A5. DagaareDagaaremorphology Chi
3.412021A4. SaukSaukgeneral Chi
23.992021R2.4. HmongHmongsemantics Hellsten
7.512021R2.1. KakawinKakawingeneral Salter
11.292021R2.5. TawalaTawalageneral Hellsten
7.212021R2.3. AinuAinugeneral Neacsu
3.162021R2.2. Hawu and DhaoHawu & Dhaogeneral Hochstein
0.762022#1Swedishgrammar Hellsten
0.812022#2Buhidscript Verhoeven
0.712022#3Italiangrammar Barron
0.842022#4Maltesegrammar Salter
1.322022#5Arhuacosemantics Verhoeven
1.932022#6Bislamascript Salter
3.862022#7Korowai and Haruainumbers Hellsten
1.72022#8Zunigrammar Salter
3.172022#9Tseltalsemantics/ grammar Hellsten
2.72022#10Mazatecogrammar / tones Salter
3.922022R2.1Mapudungunphonology Kajita, Kazune Sato (Japan 21)
7.172022R2.2Wik-Mungkancompounds Chi
4.502022R2.3Niueangrammar Hellsten
8.142022R2.4Dinkamorphophonology? Hellsten
8.362022R2.5Taosgrammar Hellsten


Relative difficulty

The problems are classified for difficulty. Here’s how this was calculated:

  • For problems from 2012 and later, the grading is objective and reflects the average marks of hundreds of competitors. Informally, the difficulty is the difference between the maximum possible mark and the average mark; so if everyone scores 100%, the difficulty is 1, but if the average is just 10%, the difficulty is 10. But as you’ll see below, it has to be more complicated than that!
    • Mathematically, the difficulty (diff) of a problem is the maximum score for that problem divided by the average score;
      • e.g. if the maximum was 20 and the average was 10, diff would be 2.0.
      • If everyone achieved the maximum, diff would be 1.0.
      • If the average was very low, say 1/20, diff would be 20.
    • However, difficulty depends not only on the problem but also on the competitor, so a problem which would be very hard for a Foundation competitor might be quite easy for an Advanced one. The figure for diff is therefore standardised for a typical Advanced competitor:
      • Where a problem was part of the Advanced competition in Round 1, diff is calculated as above.
      • Problems which were only included at lower levels (Breakthrough, Foundation or Intermediate) had their diff reduced by a figure based on the problems which were taken both at these levels and at higher levels, including Advance levels.
        • E.g. if an I-level problem’s average score was 5/10, giving an I-level diff of 10/5 = 2,
        • and the same competitors scored half (0.5) as well as the Advanced competitors did on the problems that they both did, giving an ‘I-adjustment’ for I and A (the mean I and A scores for those problems) of I/A = 0.5
        • then its diff (for a typical A-level candidate) was 2 x 0.5 = 1.
        • Similarly for lower levels: so the diff of a Breakthrough problem is given by B x F x I where
          • B = the diff for Breakthrough candidates
          • F is the F-adjustment figure (F/I) for problems taken at both F and I level
          • I is the I-adjustment figure (I/A) for problems taken at both I and A level.
        • This standardization calculation explains why some diff figures are below 1.0 (which would otherwise be the lowest possible).
      • Problems from Round 2 had their diff increased by a figure based on the difference between the Round 1 figures for the winners (who eventually took Round 2) and the overall average.
        • E.g. if the R2 diff for a problem was 2,
        • and the R1 Advanced winners’ average score was twice the average for all Advanced competitors,
        • then its diff for a typical A-level candidate was 2 x 2 = 4.