Zombie Attack

Oh no, zombies are attacking your house!

Every second, a new zombie drops down on one of the 9 spots of your lawn, which is currently unoccupied. All zombies move towards your house on the left with constant speed, and each of them needs exactly 1 second to traverse a spot of the lawn. Once a zombie steps out of the lawn, it enters your house and waits there for the others (thus each zombie travels total distance between 1 and 9 spots).

Show that after some time, the total distance traversed by any 1000 consecutive zombies will be within the range of just 50 spots.

Remark: Assume your house can accommodate an unlimited amount of zombies.

Since the number of zombies on the lawn never decreases, it must stabilize at some point. Therefore after some time T, there will be exactly K zombies on the lawn at all times, 1 ≤ K ≤ 9.

Consider any 1000 consecutive zombies appearing past time T and take a picture of the lawn at the moment each of them gets dropped on it – this makes a total of 1000 pictures. Since on every picture, there are exactly K zombies, we see exactly 1000K zombies on these pictures.

Now notice that almost all of the selected 1000 zombies appear on as many pictures as lawn spots they traverse. The zombies for which this is not true are just the K zombies, which appear on the last picture. We easily see that they have traveled between 1 + 2 + … + K − 1 and (10 − K) + (11 − K) + … + 8 spots more than the number of pictures they appear on.

Similarly, on the 1000 pictures we have taken, there are K−1 additional zombies, which appear multiple times (you can see all of them on the first picture). The total number of times they show up is again between 1 + 2 + … + K − 1 and (10 − K) + (11 − K) + … + 8.

Therefore we conclude that the total distance the selected 1000 zombies travel is equal to 1000K ± {[(10 − K) + (11 − K) + … + 8] − [1 + 2 + … + K − 1]} = 1000K ± (9 − K)(K − 1).Since (9 − K)(K − 1) is a number between 0 and 16, this solves the problem.

Stuck in a Blender

You get shrunk 100 times (preserving your density), then thrown in a blender. You have 2 minutes until the blades of the blender start spinning. How are you going to escape?

If you get shrunk 100 times, but your density remains the same, your muscles will become so strong relative to your size, that you will be able to jump out of the blender. The reason is that your weight will decrease 1000000 times, but your muscle cross-section just 10000 times.

Geography Jokes

Who says science jokes are not funny? Below you can see some of the best Geography jokes we know, along with short explanations to the more obscure of them.

Do you know any funny Geography jokes yourself? Let us know in the comment section below.

“How did the geography student drown?”
“His grades were below C-level.”

Grades in some countries are marked with letters – A, B, C, etc. “C-level” is a word play with “sea level”.

“Where do all pencils come from?”

Transylvania in Romania is supposedly the place where all vampires come from.

A giant destroyed 3 countries the other day. He picked up Turkey, dipped it in Greece, and then fried it in Japan.

The joke sounds like “A giant destroyed 3 countries the other day. He picked up a turkey, dipped it in grease, and then fried it in a pan.”

“What is smarter – longitude or latitude?”
“Longitude – it has 360 degrees.”

Latitude has 180 degrees in total, longitude has 360.

“Why do paper maps never win poker tournaments?”
“Because they always fold.”

In poker folding is forfeiting the current hand.

“What do fish and maps have in common?”
“They both have scales.”

“What is round on the ends and high in the middle?”

O-hi-o is a state in the US.

“Where is it 90 degrees, but it is never hot?”
“The North and the South pole.”

The North and South poles are located on +90 and -90 degrees latitude.

“What did Delaware?”
“A New Jersey.”

Delaware and New Jersey are US states. The joke sounds like “What Dela wear? A new jersey.”

“What do you call the little rivers which flow into the Nile?”

“What sort of pudding roams wild in the Arctic circle?”

Moose (sounds like the dessert mousse) can be seen in the arctic circle.

“What did the sea say to the shore?”
“Nothing, it just waved.”

“Where do fish keep their money?”
“In riverbanks.”

River bank is the land alongside the bed of a river.

“What do you call a country that looks like one thigh?”

Taiwan sounds like “thigh-one”.

“What do you call a stoner’s wife?”

The river Mississippi sounds like “Mrs Hippy”.

“What city always cheats at exams?”

Peking, the capital of China, sounds like “peeking”.

“Which is the pirates’ favorite country?”

“Aaarrrgghh!” is a famous pirate’s exclamation.

“Why does the Boogeyman know all the map symbols?”
“Because he is a legend.”

The legend on the map describes the meanings of all symbols.

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