Can You Solve Alice’s Crazy Clock?

A Fun Brain Teaser

Hearken, fair dreamer, to a riddle born of wonder and whimsy.
In Alice’s slumbering realm there standeth a clock, not of mortal make,
but a mad device whose hands dance to no earthly tune.

At the stroke of twelve do both its arms repose together,
united as twins beneath the solemn moon.
Yet soon, the nimble minute hand taketh flight,
whirling sunwise through the heavens,
five full circuits it maketh, sometimes fleet as thought,
sometimes slow as sorrow’s sigh,
till once again it greeteth twelve.

Meanwhile, its somber sibling, the hour hand,
turneth contrariwise, widdershins against the flow of time,
completing four proud journeys in the selfsame span,
till it too returneth to the seat of its beginning.

Now, gentle soul, attend this question of curious art:
How oft within this spell of turning do the two hands cross paths,
meeting as fated lovers, parting as strangers,
passing through one another in their mad ballet?
Mark ye well,
count not the first kiss at dawn nor the last at twilight’s end,
but all the crossings betwixt the start and finish.

What number, pray, doth their strange courtship reveal?

Alright. Let’s rephrase the problem in simple English.

There is a crazy clock in Alice’s Dream, it has two hands initially pointing at 12. The minute hand moves clockwise, making 5 rounds (with varying speeds) and comes back to 12. In the same time, the hour hand goes anti-clock wise, finishing 4 rounds and returns to 12. How many times did the two cross each other ? (Cross means meet & pass through, hence ignore start & end)

Now really give this time and think through your approach.

When you area ready, keep reading for the solution!

Solution

It’s quite a cool puzzle that tests your spatial reasoning more than math.

Here’s an analogy to get started.

If I walk past you, it also means you walk past me.

In a similar fashion, when the minute hand crosses the hour hand, the hour hand crosses the minute hand.

So let’s think relatively.

To the minute hand, the hour hand seems to move backwards even faster — by a total of 4 + 5 = 9 total turns.

Each full turn brings one meeting, except the first and last (start and end).

This means they cross each other exactly 9 − 1 = 8 times.

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