Question

В полночь на подоконнике стояли в ряд (слева направо) герань, крокус и кактус. Каждое утро Маша, вытирая пыль, меняет местами цветок справа и цветок в центре. Днем Таня, поливая цветы, меняет местами тот, что в центре, с тем, что слева. В каком порядке будут стоят цветы вечером через 37 дней?

Answer 1

герань крокус и кактус

Answer 2

Problem Analysis

In this problem, we are given a sequence of three flowers on a windowsill: geranium, crocus, and cactus. Every morning, Masha swaps the flower on the right with the flower in the center. During the day, Tanya swaps the flower in the center with the one on the left. We need to determine the order of the flowers on the windowsill after 37 days.

Solution

To solve this problem, let's analyze the pattern of flower swaps over time.

1. Initially, the flowers are arranged as follows: geranium (G), crocus (C), and cactus (K). 2. After the first morning, Masha swaps the flower on the right (K) with the flower in the center (C). The new arrangement is G, K, C. 3. During the day, Tanya swaps the flower in the center (K) with the one on the left (G). The new arrangement is K, G, C. 4. The next morning, Masha swaps the flower on the right (C) with the flower in the center (G). The new arrangement is K, C, G. 5. During the day, Tanya swaps the flower in the center (C) with the one on the left (K). The new arrangement is C, K, G.

From this analysis, we can see that the flowers follow a repeating pattern every two days: GKC, KGC, CGK, GCK, KCG, CGK, and so on.

To determine the order of the flowers after 37 days, we need to find the remainder when 37 is divided by 6 (the length of the repeating pattern). The remainder will tell us which arrangement from the pattern to use.

37 divided by 6 is 6 with a remainder of 1. Therefore, after 37 days, the flowers will be arranged in the same order as after 1 day, which is GKC.

Answer

After 37 days, the flowers will be arranged in the order: geranium, crocus, cactus (GKC).

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