Hundred-Meter Cookie
– STROOPWAFEL
In the 2016 Olympics, eleven countries competed in the Hundred-Meter Cookie event. They were seeded alphabetically, with Bulgaria first and Zimbabwe eleventh. After the event, the competitors spoke to reporters. Those who placed strictly worse than their seed position were bitter, so every sentence they said to reporters was a lie, while the others told only the truth. In addition, they knew the placing order of those who finished ahead of them, but knew nothing about the ordering of those who finished worse than them. No one made any statement whose truth value they didn't know.
Bulgaria: I saw a country with Republic in its name place ahead of me.
Cambodia: I know which of Bulgaria and Ethiopia placed better.
Central African Republic: Zimbabwe beat Italy.
Colombia: Italy beat Germany. Germany beat Cambodia.
Czech Republic: I finished better than Philippines. Bulgaria beat Zimbabwe.
Ethiopia: Cambodia finished better than me.
Germany: I don't know the relative placing of Cambodia and Ethiopia.
Italy: Suriname beat Zimbabwe.
Philippines: Central African Republic beat Ethiopia.
Suriname: I beat Czech Republic, Ethiopia, and Philippines.
Zimbabwe: Ethiopia beat at least one of Bulgaria, Cambodia, or Suriname.
To solve the puzzle, you need to determine the order in which the countries finished, which is tied to figuring out which is lying. Overviewing one possible path to solution:
- Bulgaria can only tell the truth if they won, but they claim something that contradicts winning; thus Bulgaria was not in 1st place, and additionally finished ahead of all countries with Republic in their name.
- If Cambodia is telling the truth, one of Bulgaria and Ethiopia finished ahead of them; but additionally, they have to be top 2 in order to tell the truth. The only such configuration possible is Ethiopia in 1st, Cambodia is 2nd, but then Ethiopia's claim of losing to Cambodia would be false, even though the 1st place team is a truth-teller. So, Cambodia is lying.
- That directly contradicts Philippines, so they must have finished in the bottom 2.
- Additionally, it means that Ethiopia is telling the truth, so finished in the top 6.
- If Central African Republic is telling the truth, they must be top 3, with Zimbabwe ahead of them. If Zimbabwe is top 2, they are telling the truth, with Ethiopia ahead of them. But Ethiopia can't be 1st place, so Central African Republic is lying, and Italy beat Zimbabwe. we also know that Italy beat Central African Republic, or Central African Republic's statement would be a guess rather than a lie.
- If Colombia were lying, Cambodia would have beat Germany, and Germany would have beat Italy; additionally, to avoid guessing, Germany beat Colombia. We already know that Italy beat Zimbabwe, and that Philippines is bottom 2, so that gives us 4 countries under Germany, so Germany would be telling the truth; but then Germany would have to be beating Cambodia, a contradiction. So, Colombia is telling the truth.
- This means Colombia is top 4, and Italy is ahead of Germany in the top 3, so both Italy and Germany are telling the truth.
- Because Italy is telling the truth, Suriname beat Italy, so the top 4 must be Suriname, Italy, Germany, Colombia.
- Now, the only way for Czech Republic to be telling the truth is if it came in 5th; but it also needs to finish behind Bulgaria to be telling the truth, so this is impossible. This means it finished worse than the Philippines, who are bottom 2, so Czech Republic came in last, and Zimbabwe beat Bulgaria.
- Zimbabwe always had to be telling the truth; we now know that Ethiopia can't be beating Cambodia or Suriname, so it is beating Bulgaria.
- At this point, if we exclude Zimbabwe, we know the order is Suriname, Italy, Germany, Colombia, Cambodia, Ethiopia, Bulgaria, Central African Republic, Philippines, Czech Republic. Zimbabwe has to be above Bulgaria, but if it were ahead of Ethiopia, Ethiopia would have lied, so it is between those two.
Thus, the final order is:
Suriname
Italy
Germany
Colombia
Cambodia
Ethiopia
Zimbabwe
Bulgaria
Central African Republic
Philippines
Czech Republic
Reading down the diagonal, you get STROOPWAFEL