Some of the most creative entries in our Gardner contests will be posted here.

For the first contest, I got two entries that solved the problem relativistically. I’m a philosopher by training, so I dug this one from F. Pi. of Vienna.

Sipping their cups of coffee after lunchbreak, three scientists of the famous Brownlow Institute discuss the experiment of Professor Slapenarski:

The scatterbrained physicist says:
Well, we have relative step-speeds here, so lets apply some sort of ‘Relativity-Theory’.
the factor c= (speed of professor/speed of escalator) we set to 1 (as we always like to do,you know;-) and perform some ‘renormalization’ later, if needed… soo: 50 steps down with double speed then makes a 100 steps in total, voila!

ähm, sorry, just forgot the renormalization process:
going up 5 times faster with one step down simultaneously(escalator) then would give 100*5/4 = 125 steps up. that fit’s perfect! no correction-term needed;-))

The mathematician just scribbles: L = (6*ups)/(5+ups/downs) = 100 steps. QED.

The philosopher, after ruminating for three days on the problem, came to the conclusion, that “…. so that it really could be 100 steps in total.”

The winner was W.H. with a hilarious poem, also solving via relative movements:

Suppose that the escalator connects floors 3 and 2,
and that more escalators connect the building through.

Let’s further add this additional supposition:
that when the Prof starts going up, he has some competition.

A humble janitor of the name Stanley Spadowski
starts at the same place and goes down at rate Slapenarski.

(And when we say “rate Slapenarski” we mean
that he goes down at the exact same rate we’ve seen.)

Finally, let’s say that Stanislaw tries to be extra manly:
he doesn’t stop climbing until floor 1 meets Stanley.

(Though these additions might seem rather deranged,
you have to admit that the floor height is unchanged.)

And now we ask for just one piece of datum:
Where is the prof when the custodian hits the bottom?

Well, we know that his speed is five times as shifty,
so when Stanley’s moved 50, Stanislaw’s moved 250.

At half of that Stanislaw had just reached floor three,
so he should be exactly on floor four, you see.

To sum up: the men are now separated by three floors,
have made in total 300 steps and no more.

A simple division means (unless we have blundered)
the height of one floor must be exactly… 100.

The second contest saw some cool graphic entries.

J.D.’s is reminiscent of a subway map.

H.P. sent me fifteen different images for each step, with color coded fuel levels. I’ve collapsed them into an animated .gif.

Finally, the winner, A.M. with Our “Plan”

On the Absent Minded Teller question…

I got a response caught in my spam filter, sadly.

I fished it out, because it’s an MS-Paint wonder.

For the The Fork in the Road…

Hundreds of answers poured in.

This respondent gets credit for finding a Dr. Who connection:

This situation arose in the classic Tom Baker “Doctor Who” story “Pyramids of Mars,” so I can’t really take credit for answering correctly. Anyway, the question the logician would ask is: “Knowing I want to get to a village, would a member of the other tribe tell me to take this fork?”

If the path the logician gestures towards is the one that reaches the village, the truth-tellers will answer, truthfully, that their lying counterparts would say “no, that is the wrong path;” and the liars will answer, incorrectly, that their truth-telling counterparts would say “no, that is the wrong path.”

If the path the logician gestures towards is not the one that reaches the village, the truth-tellers will answer, truthfully, that their lying counterparts would say “yes, that is the right path;” and the liars will answer, incorrectly, that their truth-telling counterparts would answer “yes, that is the right path.” (A 4-square box would make this clearer but I’m not going to go mocking up an attachment.)

So, if the answer is, “my counterpart would say that is the wrong path,” the path does reach the village; and if the answer is, “my counterpart would say that is the right path, the path does not reach the village.

While not working in context of the question, it’s worth something:

The question to ask is: Where do you live?

Both the liar and truth-teller will point you to the truth-teller village.

Can anyone explain this to me?

Which branch would you have told me lead to the village yesterday?

I’ll close out with my personal favorite. A kind of… “Wow” moment for me.

Here’s my answer: Ask “Are you a fish?” I’m assuming of course that these are tribes of humans or otherwise non-aquatic creatures.

Week 5: The Amorous Bugs

This puzzle well, puzzled a lot of people.

But I got a couple of great poems, and, of course, the winning video entry.

Nick went both ways with his solution:

lets see…..the length of a congruent logarithmic spiral in a square = r*sqrt2
r=1/sqrt2 x 10 so….
4 little bugs in a square
From each other 10 inches to start
They crawl at a rate
The same to their mate
And travel as far as aparted
(10 inches)

J.P.L. proved it.

The distance each bug traverses to the meeting point must be exactly the same as the distance originally separating each bug from its target bug: ten inches.

Proof:
Given the symmetrical original position and the fact that the bugs crawl at the same constant rate, it follows that, during the trip, the trajectory of each bug at any instant will be perpendicular to the trajectory of its target bug at that instant (e.g., as bug A turns to follow bug B, D will adjust its path to the same degree as A). Now, suppose the distance traversed by D is less than or greater than ten inches. Then bug A must have moved toward or away from bug D, or bug D must have deviated from the most direct route. But bug A is always traveling perpendicular to bug D, so bug A cannot have moved toward or away from bug D. For the same reason, bug D cannot have deviated from the most direct route to bug A. So, the distance traversed by D cannot be less than or greater than ten inches. It must therefore be ten inches.

Sarah wrote a poem…

“Follow the leader”, said A to D,
“But who’s the leader, you or me?”
“It matters not”, said crafty A,
“If at the corners we all stay”
“We’ll always make a square”, said he,
“Though it will shrink, as you will see
“And in ten inches time we’ll be,
“Together, orgiastically.”

…that worked the word “orgiastically” in seamlessly. That is an achievement.