Spoiler in brief for those who don't know the ending yet:
At the end, Phileas Fogg alongside with his companions realize that they have arrived back to London a day earlier than expected due fact the party did travel eastward.
Each time they crossed the known time-zone(s), they adjusted their (pocket-)clocks an hour backwards (sans Passepartout. depending on the adaptation / source), which each time roughly gave them an extra hour to win the wager (the details regarding to "won" amount of time differs a bit in each adaptation of the novel).
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That famous ending should be a quite simple one.
But how about something a bit more modern with essentially same result, only the whole process lasts over an year (using a real, up-to-date-calendar will help during "perceiving"-phase:
- You're being paid exactly every-fourth-full-week on Friday (E.G. during 2015 first on February 27th, then on March 27th, then on April 24th, and so worth).
+ On those paydays, you also start paying your apartment-rent upfront (E.G. on the payday of February 2015, you're paying the rent of March 2015, and so forth).
-> By continuing paying the rent like this for roughly 12-months (less even, to be precise), you will end up into a situation in which you're paying the upcoming rent over a month before hand (E.G. on February 2016, you're already paying the rent of April 2016).
For the sake of information-sharing alongside providing yet even more material to help with "perceiving"-phase, here is a link to an example "payday-model" from real-life:
Labour Market Subsidy in Finland
As the title of this question hints, I am indeed looking a term / name for "mathematical-phenomenon" alongside a simple as possible formula for simple people.
Loosely, I would call this "phase shift".
Suppose we have two periodic phenomena of different frequencies or equivalently different periods. If both start at the same time, "in phase", then after some time the two cycles will be significant out of sync, "out of phase".
Eventually the two will be close to or exactly back in phase in as much as the two phenomena begin their cycles at the same time. But the number of periods that has elapsed is not the same for the two.
In physics, this behavior receives a lot of quantitative attention as many physical systems are modeled as the superposition of waves with different periods.