Question

Eight children, of which four girls (Barča, Gabika, Klára, Táňa) and four boys (Janko, Libor, Pavol, Radko), were lined up in two rows, in two groups (left and right) in four rows. They played silent mail and everyone could pass a message to either the child next to them or the child behind them. There were five transmissions before the message got from one of the children in the first row to the first of the children in the fourth row. We know that: ·The handover of the report took place between the children in the following order: Barča- Janko-Libor-Klára-Gabika-Pavol. Barča stood in the first row, but she did not stand in the same crowd as Klára. ·Janko stood in the left crowd. Who could stand in the same row as Paul? (A) only Radko (B) just anyone from Táňa, Radko (C) just anyone from the couple Gabika, Táňa (D) anyone from the trio Gabika, Táňa, Radko

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Answer to a math question Eight children, of which four girls (Barča, Gabika, Klára, Táňa) and four boys (Janko, Libor, Pavol, Radko), were lined up in two rows, in two groups (left and right) in four rows. They played silent mail and everyone could pass a message to either the child next to them or the child behind them. There were five transmissions before the message got from one of the children in the first row to the first of the children in the fourth row. We know that: ·The handover of the report took place between the children in the following order: Barča- Janko-Libor-Klára-Gabika-Pavol. Barča stood in the first row, but she did not stand in the same crowd as Klára. ·Janko stood in the left crowd. Who could stand in the same row as Paul? (A) only Radko (B) just anyone from Táňa, Radko (C) just anyone from the couple Gabika, Táňa (D) anyone from the trio Gabika, Táňa, Radko

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Nash

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87 Answers

Pred vyriešením úlohy si najskôr uvedomme niektoré faktory. Vo východiskovom stave máme dva zástupy, každý pozostávajúci zo štyroch rád. Z toho vieme, že Pavol stojí v jednom zástupe a že Janko stojí v ľavom zástupe. Taktiež vieme, že medzi Barčou a Klárou nie je možné, aby stáli v rovnakom zástupe.
Ak poznáme poradie odovzdania správy medzi deťmi, môžeme tento fakt využiť na určenie možných umiestnení detí v zástupoch.

Podľa zadaného poradia odovzdania správy vieme, že Barča odovzdala správu Jankovi, Janko odovzdal správu Liborovi, Libor Kláre, Klára Gabike a Gabika Pavlovi. Musíme teraz preskúmať, v akej časti zástupu mohla daná schéma z odovzdávania správ nastávať.

Môžu existovať nasledujúce prípady:
1) Ak Janko stojí v ľavom zástupe, potom Barča musí stáť vpravo od Janka, aby mohla odovzdať správu. To znamená, že Klára sa musí nachádzať v ľavom zástupe. Z toho vyplýva, že Gabika sa musí nachádzať v pravom zástupe.
2) Ak Janko stojí vpravo, potom musí Barča stáť vľavo od Janka. Z toho vyplýva, že Klára musí stáť vpravo od Barči a Gabika v ľavom zástupe.

Z týchto dvoch prípadov nám vyplýva, že Gabika a Pavol nemôžu mať rovnaké umiestnenie v rade.
Takže správna odpoveď je (D) ktokoľvek z trojice Gabika, Táňa, Radko.

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