Úloha ID 1603 - 
Závod je dlouhý 7 km a má význačné body dle následující tabulky, kde čísla udávají vzdálenost od startu.
| Hospoda H | Rybník R | Křižovatka K | Cíl C |
| 1,2 km | 2,5 km | 4,7 km | 7 km |
Dále jsou na trase tři kontroly. Vzdálenost mezi druhou a třetí kontrolou je dvakrát menší než mezi první a druhou kontrolou. Od třetí kontroly do cíle zbývá 1/7 závodu. Kontroly jsou umisťovány po celých kilometrech. První kontrola není na startu. Které z následujících tvrzení je určitě pravdivé?
Správná odpověď je: A
Šly by použít i soustavy rovnic, ale podmínek je tak málo, že úlohu můžeme vyřešit z hlavy. Třetí kontrola je jednoduše v 7 – (7/7) = 6 km trasy. Chceme, aby vzdálenost prvních dvou kontrol byla dvojnásobná oproti dvěma posledním, a zároveň pamatujeme na požadavek, že se kontroly nacházejí na celých kilometrech. Máme tedy k dispozici kilometry 1–5. Vzdálenost prvních dvou kontrol musí být sudé číslo, aby polovina byla pořád celé číslo. 4 + 2 > 5 km, které máme k dispozici. Proto je první kontrola na 3. kilometru, druhá na 5. a třetí na 6. kilometru. Lze si též všimnout, že pozici třetí kontroly známe hned, a že A je správně, lze rozhodnout bez výše uvedeného postupu.
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