Úloha ID 1602 - 
Závod je dlouhý 8 km a má význačné body dle následující tabulky, kde čísla udávají vzdálenost od startu S.
| Start S | Penzion P | Kaplička K | Skála S |
| 0 km | 1,25 km | 2,5 km | 4,6 km |
Na trase jsou tři kontroly. Vzdálenost první kontroly od startu je stejná jako dvojnásobek vzdálenosti poslední kontroly od cíle a druhá kontrola leží přesně uprostřed mezi první a třetí kontrolou. Kontroly leží vždy na celém kilometru. Které z následujících tvrzení je určitě nepravdivé?
Správná odpověď je: D
Můžeme si pomoci soustavou rovnic: označíme si postupně úseky trasy mezi startem, jednotlivými kontrolami a cílem jako W, X, Y, Z. Například Y leží mezi předposlední a poslední kontrolou. Platí, že W + X + Y + Z = 8. Z první podmínky platí W = 2 · Z a z druhé X = Y (druhá leží uprostřed, tedy vzdálenost je stejná oběma směry). Po dosazení do první rovnice dostaneme 3Z + 2X = 8 a jako řešení hledáme pro X, Z celá kladná čísla. Je zřejmé, že 3 · 2 + 2 · 1 = 8, tedy Z = 2, X = Y = 1 a W = 4. První kontrola se nachází 4 km od startu, druhá 5 km a třetí 6 km od startu, tedy skála leží mezi první a druhou kontrolou.
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