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. You can also download the same list as an Excel spreadsheet; this is not locked, so once you’ve saved it locally, you can easily search it, edit it or re-sort the data. In both lists, each problem’s name has a link to the downloadable problem.  

Each problem is listed with the following information:

  • 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
    • this cell is hyperlinked to a file containing the problem concerned, a separate answer sheet (where relevant), and the correct answers, plus a mark scheme and detailed directions for marking (as used by the original markers).
  • language: the language(s) from which its data are taken
  • extras?: any information beyond the problem and its solution.
    • expanded: an extended essay-length discussion of the problem and how to solve it, as well as ideas for building on it in discussing more general ideas about language and linguistic analysis.
    • notes: brief notes on the problem data, possibly as a separate file from the problem file.
    • problem, solution, commentary and marking scheme: a single file containing all relevant information.


The problems

The problems are listed below in increasing order of difficulty.Note that:

  • 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.
  • 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 difficulty you can order by year, starting either with the oldest or the youngest.
  • 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.

The problems are also listed in a downloadable spreadsheet which you can edit in Excel like any other spreadsheet. Moreover, unlike the list below, this spreadsheet also includes clickable links to the downloadable problem files, so if you want to download the files, you need the spreadsheet.

The table of problems

diffyearnumber, namelanguageextras?areaauthor  
0.520112. JapaneasyJapaneseexpandedscriptHarold Somers
0.5420143. MokileseMokileseexpandedgeneralJeff Siegel
0.6720141. What time is it in Tallinn?EstonianexpandedgeneralBabette Newsome
0.71201818.1 (In)definitely RomanianRomaniannotes and solutiongeneralJulia Barron
0.81201818.2 Lithuanian road tripLithuaniannotes and solutiongeneralBabette Newsome
0.837212794608162019P2 JapaneseJapanesenotesscriptBabette Newsome
0.8584002799328120162. ForeignFrench, German, Spanishproblem, solution, commentary and marking schemecomparativeDick Hudson
0.8920121. Being with it in YolmoYolmoexpandedgeneralLauren Gawne
0.92017R1.3. We are all European9 languagesnotes and solutioncomparativeBabette Newsome
0.9220122. Danish numbersDanishexpandednumbersMike Swan
0.948758666184620164. Beijing subwayChineseproblem, solution, commentary and marking schemescriptCatherine Sheard
120101. Sorry we have no red cucumbersFrenchsyntaxDragomir Radev
120102. Gelda’s House of GelbergargEnglishgeneralCindy Schneider
120103. Say it in AbmaAbmageneralLuda Kedova & Rachel Nordlinger
12010R2.3. F u cn rd thsEnglishcomputingRichard Sproat
1.003985993068320161. AlphabetGreekproblem, solution, commentary and marking schemescriptDick Hudson
1.01630118975172019P3 JahaiJahainotesmeaningBabette Newsome
1.052017R1.1. Our Italian familyItaliannotes and solutionmorphosyntaxDick Hudson
1.0620151. Counting in KarelianKareliannumbersGraeme Trousdale
1.0820142. Maori loanwordsMaorinotesgeneralPat Littell
1.1720126. Crocodile BardiBardigeneralCatherine Sheard
1.182017R1.5. Basquing in the sunBasquenotes and solutionmorphosyntaxAleka Blackwell
1.19201818.5 At Ease in GilberteseGilbertesenotes and solutiongeneralMichael Salter
1.220138. A little Dutch problemDutchgeneralHarold Somers
1.251620226025920169. NhandaNhandaproblem, solution, commentary and marking schemegeneralBabette Verhoeven
1.2620146. Kairak verbsKairaknotesgeneralCindy Schneider
1.2620152. Georgian placesGeorgianscriptDaniel Rucki
1.28201818.3 Finding your way in SofiaBulgariannotes and solutionscriptBabette Newsome
1.293199554069120168. SomaliSomaliproblem, solution, commentary and marking schememorphologyHarold Somers
1.30642352942372019P4 WelshWelshnotesmorphosyntaxBabette Newsome
1.3220153. Polish your PolishPolishgeneralDaniel Rucki
1.34797117397342019P5 PitjantjatjaraPitjantjatjaranotesgeneralRebecca Dafina and Wilmoth
1.3620123w. Welsh librariesWelshnotesgeneralDick Hudson
1.367521367521420166. KaqchikelKaqchikelproblem, solution, commentary and marking schemegeneralMichael Yoshitaka Erlewine
1.3820144. Running speechEnglishnotesphonetics, scriptSue Barry & Dick Hudson
1.392017R1.4. A little TshilubaTshilubanotes and solutionmorphosyntaxTom McCoy
1.400495469448820163. WatsoniumIrishproblem, solution, commentary and marking schemespelling of loansJane D’Altuin and Harold Somers
1.422017R1.2. Inuktitut scriptInuktitutnotes and solutionscriptOllie Sayeed
1.436806737837520165. AmeleAmeleproblem, solution, commentary and marking schemegeneralBabette Verhoeven
1.4420135. BulgarianBulgariansyntaxBozhidar Bozhanov
1.4880049272452019P1 LadinLadinnotesgeneralJulia Barron
1.49973324612882016R2.1 MalayMalayProblem, solution and markinggeneralBozhidar Bozhanov
1.5120154. Old EnglishEnglishgeneralGraeme Trousdale
1.557482517482520167. The strange case of the Estonian languageEstonianproblem, solution, commentary and marking schemegeneralPraveen Venkataramana
1.5620131. YodaspeakEnglishsyntaxHarold Somers
1.5920128. Arcturan intergalactic peace messagefictitious languagegeneralSimon Zwarts
1.5920155. Elder FutharkNorsescriptCatherine Sheard
1.6920127. Waorani numbersWaoraninumbersDrago Radev
1.722012R2.2. Who is good?LuiseñogeneralRonald Langacker (via Dick Hudson)
1.7620124. HaitianHaitian notesgeneralIvaylo Youmerski
1.7620158. Can you finish Finnish?FinnishgeneralBabette Newsome
1.772017R1.6. Maori for the beachMaorinotes and solutiongrammarAleka Blackwell
1.772017R1.8. ChoctawChoctawnotes and solutionmorphosyntaxBabette Newsome
1.7920136. The long and short of English verbsEnglishnotesgeneralDick Hudson
1.81560506693022019P7 HarmongolianMongoliannotesmorphophonologyEthan Chi
1.83485703616622016R2.2. TocharianTocharianProblem, solution and markinghistoricalOllie Sayeed
1.9320125. EsperantoEsperantogeneralAlexey Pegushev
1.95201818.6 Are you OK with N’ko?Nkonotes and solutionscriptBabette Newsome, Harold Somers
1.96201818.4 What's yours is mine (for eating)Fijiannotes and solutiongeneral??
22010R2.1. Ardhay UzzlepayMinangkabaugeneralDiego Molla-Aliod
220117. The war of the dotsEnglish (braille)scriptPatrick Littell
22011R2.1. Stopping and flapping in WarlpiriWarlpirigeneralMary Laughren
22011R2.2. Counting in IrishIrishnotesnumberTom Payne
220111. Running on MTEnglishmeaningHarold Somers
220113. Doubling in Caterpillar CountryArrerntenotesgeneralMark Dras & Mary Laughren
220115. Mix up on the farmPapagogeneralLori Levin (data from Ken Hale)
220116. Tiger taleIndonesiangeneralDragomir Radev
2.03706075402232019P9 NdebeleNdebelenotesgeneralMichael Salter
2.08042264325792016R2.5. Get edumacated!EnglishProblem, solution and markingphonologyPatrick Littell
2.1220133. PaliPaligeneralBabette Newsome
2.1320157. MurrinhpathaMurrinhpathageneralRachel Nordlinger
2.1689005481638201610. Don't sell the house!Nungproblem, solution, commentary and marking schemegeneralAlex Wade
2.222012R2.1. A fox among the hEnglishcomputingPatrick Littell
2.352012R2.3. The little engine that could… readEnglishlogicJames Pustejovsky, Patrick Littell
2.420129. WaanyiWaanyigeneralMary Laughren
2.462015R2.3 Do-this-do-thatHmong notesgeneralDavid Mortensen
2.5620159. Zoink!EnglishsemanticsDragomir Radev with Christiane Fellbaum and Jonathan May
2.63531377704362019R2.2 LepchaLepchanotesscriptEthan Chi
2.652017R1.9. The goat, the mother and the Abkhaz wardrobeAbkhaznotes and solutiongrammarSamuel Andersson, Oliver Sayeed, and Elysia Warner
2.7201818.7 Icelandic RelationsIcelandicnotes and solutiongeneralBabette Newsome
2.7420156. Japanese placesJapanesegeneralHarold Somers
2.75494476734532016R2.4. DevanagariDevanagariProblem, solution and markingscriptLauren Gawne
2.7663998391432016R2.3. HuliHuliProblem, solution and markingnumbersBill Huang
2.842017R2.1. NepaliNepalinotes and solutiongrammarBabette Newsome
2.882017R2.3. VietVietnamesenotes and solutiongrammarJames Hyett
2.93694372750882019P10 BrailleEnglishnotesscriptBabette Newsome
2.9920145. TurkishTurkishnotesgeneralDavid Palfreyman
320104. Lost in YerevanArmenianscriptDragomir Radev
320107. Texting, texting, one two threeEnglishcodePatrick Littell
32010R2.2. Be Cree-ativeCreescriptPatrick Littell & Julia Workman
320106. Tangkhul tangleTangkhulgeneralDavid Mortensen
32010R2.4. Tale of KieuVietnamesescriptDavid Mortensen
32010R2.5. Possessed in VanuatuVanuatugeneralJane Simpson & Jeremy Hammond
320114. Ulwa possessivesUlwanotesgeneralRichard Sproat
3.01447210031432019R2.1 AfrihiliAfrihilinotesgeneralMichael Salter
3.062012R2.5. Catalan pluralsCatalanmorphophonologyBoris Iomdin
3.22017R1.10. Kaytetye kinshipKaytetyenotes and solutionsemanticsMyfany Turpin
3.2420147. IlokanoIlokanonotesgeneralBozhidar Bozhanov
3.2920139. BengaliBengalinotesgeneralBozhidar Bozhanov
3.322017R2.2. Do you see what I see?Proto-Algonquian notes and solutionmorphosyntaxDaniel Lovsted
3.3920123d. Dutch past participles DutchnotesgeneralBabette Newsome
3.4920134a. Arabic scriptArabicnotesscriptDavid Palfreyman
3.632015R2.2 Malagasy crossnumberMalagasy notesnumbersTom McCoy
3.64107018763032019P6 CippusAbellanusOscannotesscriptMichael Salter
3.9820149. LontaraBuginesenotesscriptChelsea Voss
3.98225192975472019R2.4 CupenoCupenonotesgeneralDaniel Lovsted
42011R2.5. Swallow the saltTadaksahakgeneralBozhidar Bozhanov
4.022017R2.4. Muddled hieroglyphsEgyptiannotes and solutionscriptDick Hudson
4.232017R1.7. On the right Tamil trackTamilnotes and solutionscriptKai Low
4.352017R2.5. Magic Yup’ikYup'iknotes and solutionnumberKai Low
4.612014R2.1. Kiswahili verbsKiswahiligeneralCatherine
4.64201818.R2.4 It’s true: The truth about Chalcatongo Mixtec Mixtecnotes and solutiongeneralBabette Newsome
4.67652611487642019R2.5 Witsuwit'enWitsuwit'ennotesgeneralDaniel Lovsted, Sam Ahmed, Ellie Warner
4.84595226551282019R2.3 PolishPolishnotesmorphophonologyMs Veneva
520105. Turkish delightTurkishgeneralBozhidar Bozhanov
52011R2.3. Axolotl in the waterNahuatlgeneralJohn Berman
52011R2.3. A script for the NdyukaNdyukascriptPatrick Littell
5.07201818.R2.2 NivkhNivkhnotes and solutiongeneralHeather Newell
5.3201818.R2.3 MenyaMenyasolutiongeneralAleka Blackwell
5.632013R2.4. Stockholms TunnelbanaSwedishgeneralPatrick Littell
5.742013R2.1. Deer FatherQuechuageneralPatrick Littell
5.93201818.8 Vietnamese MatchingVietnamesenotes and solutiongeneralTom McCoy, Pat Littell, and Lori Levin
6.0620134s. The Shavian AlphabetEnglish – ShaviannotesscriptBabette Newsome
6.1201818.10 Tirana touristAlbaniannotes and solutiongeneralAli Sharman
6.482014R2.2. Untangling Tanghulic Kachai, Tusom, UkhrulcomparisonDavid Mortensen
6.52015R2.4 AymaraAymaraphonologyJosh Falk
6.682014R2.4. Navajo gophersNavajogeneralBabette Newsome
8.112014R2.3. Learning YidinyYidinygeneralMary Laughren
8.5820155 RomanceLatin, French, Catalan, Romanianhistorical comparisonDavid Palfreyman
8.7220137. PhoenicianPhoenicianscriptHarold Somers
9.012014R2.5. Hungarians in a fieldHungarianpuzzleAdam Hesterberg
9.432015R2.1 MaxakaliMaxakaligeneralAlex Wade
9.48201510. Georgian EraGeorgianscript, generalDorottya Demszky
9.992013R2.5. Playing the cognate gameIndonesian, SwahilietymologyCatherine Sheard
12.672013R2.3. BejaBejageneralDick Hudson
15.26201818.9 Central Pamerican sumsPamenotes and solutionnumberMilena Veneva
16.9920148. Musical codeEnglishnotescodeHarold Somers
17.5813471502592019P8 GumatjGumatjnotesnumbersEthan Chi
32.942013R2.2. Putting the books in order Georgian, ArmenianscriptDrago Radev
33.332012R2.4. 100 surnamesPhags-pascriptPatrick Littell


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.