Suppose you have a time machine that can only jump to leap days. What’s the chance that a random jump will put you on a Monday? [Maths]

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Here’s a puzzle for you –

Like the TARDIS, your time machine has a fault.
Like the TARDIS, your time machine has a fault. The fault isn’t a failure of its chameleon circuit, but a quirk in its ability to jump to particular dates. Picture courtesy aussiegall (Flickr), licensed Creative Commons.

You own a time machine with an unusual property: it can only travel to 29th February. It can jump to any 29th February, anywhere at all, in any year (even back before we invented the Gregorian Calendar, and far into the future after we’ve stopped using it), but it can only finish its journey on a 29th of February, in a Gregorian leap year (for this reason, it can only jump to years which are leap years).

One day, you decide to take it for a spin. So you get into your time machine and press the “random” button. Moments later, you have arrived: it is now 29th February in a random year!

Without knowing what year it is: what is the probability that it is a Monday? (hint: the answer is not 1/7 – half of your challenge is to work out why!).

Dan Q

The Leap Machine (Puzzle)

Here’s a puzzle for you –

Like the TARDIS, your time machine has a fault.
Like the TARDIS, your time machine has a fault. The fault isn’t a failure of its chameleon circuit, but a quirk in its ability to jump to particular dates. Picture courtesy aussiegall (Flickr), licensed Creative Commons.

You own a time machine with an unusual property: it can only travel to 29th February. It can jump to any 29th February, anywhere at all, in any year (even back before we invented the Gregorian Calendar, and far into the future after we’ve stopped using it), but it can only finish its journey on a 29th of February, in a Gregorian leap year (for this reason, it can only jump to years which are leap years).

One day, you decide to take it for a spin. So you get into your time machine and press the “random” button. Moments later, you have arrived: it is now 29th February in a random year!

Without knowing what year it is: what is the probability that it is a Monday? (hint: the answer is not 1/7 – half of your challenge is to work out why!).