The Large Dangerous Wolf goes to tear the Ugly Duckling to shreds except you place that noggin to make use of. Sure, I’m mixing characters from two totally different fairy story universes, however possibly the Brothers Grimm meets Hans Christian Andersen is the crossover occasion we by no means knew we would have liked.
Guaranteeing that the Ugly Duckling lives to develop into a gorgeous swan on this week’s puzzle might be fairly tough, however there’s a satisfying resolution for those who keep it up. Very like a fairy story, varied incarnations of the issue have existed in puzzle folklore for a while. When you already know the answer, please chorus from spoiling it within the feedback. I wish to give newcomers an opportunity at a shout-out and all the happily-ever-after glory that comes with it.
Did you miss final week’s puzzle? Test it out here, and discover its resolution on the backside of right now’s article. Watch out to not learn too far forward for those who haven’t solved final week’s but!
Puzzle #28: Duck Duck Go
The Ugly Duckling is within the middle of a round lake when he spots the Large Dangerous Wolf lurking on the shore. The wolf can’t swim, and the duckling can’t fly away from water (however can fly from land). The wolf patrols the skin of the lake ready for the duckling to achieve land in order that he can feast. The wolf strikes 4 occasions sooner than the duckling can swim. He can see the duckling and is free to prowl alongside the shoreline nonetheless he needs. How can the duckling make it to land and fly away with out changing into the wolf’s dinner?
As common, this isn’t a trick query. The reply isn’t “the lake is frozen so the duckling can fly away” or something like that. There’s a authentic technique with mathematical reasoning behind it. Good luck!
I’ll be again subsequent Monday with the reply and a brand new puzzle. Have you learnt a cool puzzle that you simply assume needs to be featured right here? Message me on Twitter @JackPMurtagh or e-mail me at gizmodopuzzle@gmail.com
Answer to Puzzle #27: Heads Up
Last week I requested you to research a twist on coin flips.
You and I are going to settle one thing with a coin flip. As an alternative of an bizarre coin flip, you’ll name both “HHT” or “THH”. Then we’ll flip the coin a number of occasions in a row and report the outcomes. If the sequence heads, heads, tails happens first then HHT wins and if the sequence tails, heads, heads happens first, then THH wins. We maintain flipping till one among them happens.
Which do you name? Or does it not matter?
What’s the likelihood that every wins?
THH wins 75% of the time and HHT solely wins 25% of the time, so you need to name THH. Shout-out to Enfy for the right resolution and for noticing that the winner is decided after solely two flips.
When you flip a coin thrice in isolation, the likelihood that the tosses flip up heads, heads, tails is identical because the likelihood that they flip up tails, heads, heads (each ⅛), so it’s tempting to cause that the selection doesn’t matter. However the truth that we maintain flipping till one sequence happens really modifications every thing.
If the primary two flips are each heads (which happens 25% of the time), then HHT is assured to win, however all different mixtures of first two flips (TT, TH, and HT) result in a win for THH (giving us the 75%). If the primary two flips are HH, then we both get a tails subsequent, giving HHT an instantaneous win, or we delay tails by flipping extra heads. No person wins on a string of heads, so we’ll maintain flipping till a tails happens, at which level the final three flips might be HHT.
HHT can solely win if no tails precedes it within the sequence of flips. To see this, think about a string of coin flips terminating with HHT. What coin flip instantly preceded this? If it’s tails, then THH really gained. But when it’s heads, then what preceded that? Once more a tails implies that THH really gained. So if the primary two flips are both TT, TH, or HT, then a tails has already occurred with out HHT successful, resulting in a assured win for THH.
This phenomenon generalizes. For any sequence of three flips that I declare as my win situation, you will discover a distinct sequence of three that offers you a bonus over me. Moreover, the successful sequence tends to finish with the beginning of the shedding sequence. For instance, if I declare HHH, you then’d declare THH and you’d win 87.5% of the time.