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Can You Save the Ugly Duckling from Sure Demise?

The Massive Dangerous Wolf goes to tear the Ugly Duckling to shreds until 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 wanted.

Guaranteeing that the Ugly Duckling lives to develop into a gorgeous swan on this week’s puzzle shall be fairly tough, however there’s a satisfying answer if you happen to keep it up. Very similar to 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 answer on the backside of in the present day’s article. Watch out to not learn too far forward if you happen to haven’t solved final week’s but!

Puzzle #28: Duck Duck Go

The Ugly Duckling is within the heart of a round lake when he spots the Massive 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 surface of the lake ready for the duckling to succeed in land in order that he can feast. The wolf strikes 4 instances 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 official 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 suppose ought to be featured right here? Message me on Twitter @JackPMurtagh or electronic mail me at

Answer to Puzzle #27: Heads Up

Last week I requested you to investigate a twist on coin flips.

You and I are going to settle one thing with a coin flip. As a substitute of an strange coin flip, you’ll name both “HHT” or “THH”. Then we’ll flip the coin a number of instances in a row and document 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 hold flipping till one in every of them happens.

Which do you name? Or does it not matter?

What’s the chance 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 proper answer and for noticing that the winner is decided after solely two flips.

When you flip a coin 3 times in isolation, the chance that the tosses flip up heads, heads, tails is identical because the chance 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 hold flipping till one sequence happens really modifications every little thing.

If the primary two flips are each heads (which happens 25% of the time), then HHT is assured to win, however all different combos 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 hold flipping till a tails happens, at which level the final three flips shall 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 profitable, resulting in a assured win for THH.

This phenomenon generalizes. For any sequence of three flips that I declare as my win situation, you could find a special sequence of three that provides you a bonus over me. Moreover, the profitable sequence tends to finish with the beginning of the shedding sequence. For instance, if I declare HHH, then you definitely’d declare THH and you’ll win 87.5% of the time.

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