Herman lives in a house on the Caribbean island of Kinja, where the weather is warm all year. Let’s assume all Kinjan houses are of similar construction, and no houses have a water heating system. Herman takes a shower every day at 5 pm, and at the end of his shower, he measures the water temperature coming out of the shower head. Below are the results for a 150-day period.

Water temperature grid

What is the likeliest explanation for the drops (blue) and spikes (red) in water temperature?

These fluctuations happen to all houses on Kinja, sometimes on the same days, and sometimes not.

Updates: As mentioned in the comments:

Herman’s shower takes the same amount of time every day.

Seeing "exactly" the same temperature numbers on various days is not important, and is just to simplify things. The numbers just convey drops (blue), spikes (red), and normal (black).

The following groundbreaking info was found by @oleslaw:

The houses on Kinja have cisterns.

As further info:

Cisterns are built below ground level, often where a house’s basement would be. Cisterns are common in the Caribbean islands where well water is brackish, and there is no municipal water system to pipe water to houses.

More hints:

There are two main ways for water to get into a cistern. In the more desirable way, the water is cooler than normal, and it’s free. In the other way, the water is sometimes warmer than normal, and it’s not free.

  • 1
    $\begingroup$ Does his shower take the same amount of time every day? $\endgroup$
    – Gamora
    Aug 1 '19 at 15:33
  • $\begingroup$ @Bee "Does his shower take the same amount of time every day?" Yes. $\endgroup$
    – FlanMan
    Aug 1 '19 at 15:44
  • 2
    $\begingroup$ How does the water source come from? the seawater or freshwater or groundwater? $\endgroup$
    – Conifers
    Aug 2 '19 at 1:49
  • $\begingroup$ I wonder if it is important that all the drops / spikes are exactly the same temperature-wise or that they are just drops / spikes $\endgroup$
    – oleslaw
    Aug 2 '19 at 6:12
  • $\begingroup$ @oleslaw Seeing "exactly" the same temperature numbers on various days is not important, and is just to simplify things. The numbers just convey drops (blue), spikes (red), and normal (black). $\endgroup$
    – FlanMan
    Aug 2 '19 at 13:26

Given that:

the houses on Kinja have cisterns below ground level

it might follow that the best and cheapest way to replenish the supplies is:

rainwater. A fresh rainstorm would result in free, cool water refilling the cistern. A shower shortly after rain would be cooler than normal. The temperature dips in the data come only a few days apart, representing a cloudburst every few days in Kinja's rainy season. The temperature normalises soon afterwards as the coolness of the rains wears off.

As for the rises in temperature:

After the rainy season Kinja enjoys much hotter drier weather. Water supplies get low and cisterns must be replenished manually by the homeowner before they run out. The water to achieve this must be purchased from a local merchant whose large bottles/barrels/tanks of water have been sitting out in the sun, absorbing heat. This water will thus naturally be warmer than the usual supply. To save expense water is purchased only infrequently, in larger batches, hence the longer periods of time between temperature peaks.

  • $\begingroup$ Your explanation for the temperature dips (cooler water) is completely correct. For the spikes (warmer water), your explanation of timing is correct. Your explanation for how the water got warmer is not what I intended, but it's feasible, so you get the check mark. The intended answer is, the water is warmer because rot13(gur jngre pbzrf sebz n qrfnyvangvba cynag, juvpu hfrf qvfgvyyngvba, juvpu urngf gur jngre. Gur qvfgvyyrq jngre vf gura qryvirerq gb gur ubhfr ivn gnaxre gehpx, juvyr gur jngre vf fgvyy jnez.) $\endgroup$
    – FlanMan
    Aug 5 '19 at 23:05
  • $\begingroup$ @FlanMan Aha, I see where you were coming from - probably wouldn't have guessed that precise scenario! Thanks for the checkmark, +1 for the puzzle - an interesting real-life lateral thinking puzzle... $\endgroup$
    – Stiv
    Aug 6 '19 at 5:19

This is my breakdown of the question. I couldn't find the final answer, but I hope it helps.

The story of Herman living on Kinja is a reference to

Herman Wouk's novel "Don't stop the carnival" (https://en.wikipedia.org/wiki/Don%27t_Stop_the_Carnival_(novel))

The novel takes place at fictional island named Kinja, which was owned by Great Britain.
According to the novel itself, there is a hotel on Kinja. Following the plot, there is a water shortage, which remains a major problem for the hotel keeper. Maybe his efforts to refill his cistern affect the total amount of water nearby, so the temperature differs (less water requires less heating - by the Sun), but this would not explain the fact that not all Kinjans experience this at the same days.

It is said that exactly at 5p.m. the British like to have a tea, which requires boiling the water and drinking hot beverage, so I believe the expected explanation is related to this fact. Even though the OP stated explicitly that the 5p.m. tea is not important, I believe that the 5p.m. itself plays a role here.

Feel free to use the answer above to create your own ones.

  • $\begingroup$ Realizing that the houses on Kinja have cisterns is a critical breakthrough. Tea at 5 p.m. is not important. $\endgroup$
    – FlanMan
    Aug 2 '19 at 10:11

Considering the @FlanMan's comments and the other answer

The important fact is that the houses have cisterns to store water.

  1. The cisterns can be easily heated up by the Sun.

  2. The temperature of each cistern may be different in each house, as they can be put in places that have different exposure to sunlight + the clouds.

So the fluctuations are caused because of the

Sun heating up the cisterns or clouds covering it and thus cooling.

The fluctuations may be caused by the

Kinja's weather.

The water is taken from the sea, which is heated by the Sun and cooled by the rain.
If it is raining, the water is cooler than normal and if it is unusually sunny, the water is a bit warmer.
It does not always affect all the Kinjans, because the island is large and on different parts of it there is different weather.

  • $\begingroup$ You're on the right track. $\endgroup$
    – FlanMan
    Aug 2 '19 at 10:14
  • $\begingroup$ The cisterns are below ground level, so are not quickly affected by sun or clouds. $\endgroup$
    – FlanMan
    Aug 2 '19 at 11:31
  • $\begingroup$ Perhaps the island of Kinja has a monsoon season which affects the temperature of the water from which the cisterns are drawing? $\endgroup$
    – earora4498
    Aug 2 '19 at 18:06

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