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### When Dogs Explode

Topic: science

WHEN DOGS EXPLODE

If a dog has 546 fleas, and the dog explodes, sending each flea flying along a different three-dimensional vector of random direction and of magnitude distributed between 10m/s and 100m/s (assume uniform random distribution), and one of the fleas starts squawking madly and another one says to him, "RADIO!!! RADIO!!!", what color was the dog?

Red, of course. Exploding dogs are always red.

Wrong, wrong, wrong. You didn't read the question carefully. He asked what color the dog *was*, not what color it now *is*.

Ok. We all know that fleas are fiercely territorial creatures. And that in fact each flea requires about 2.4 sq. cm of hide to coexist peacefully with other fleas on the same host. Assuming that the host dog was completely covered with fleas (i.e. had reached maximal flea bearing capacity) at the time of detonation, we can extrapolate the total surface area of the host dog with the formula:

A = f * e

Where

A = total surface area of host dog in square centimeters.

f = number of fleas found on host dog.

e = "elbow room" in square centimeters required by each flea.

Substituting, we have:

A = 546 * 2.4 = 1310.4 sq. cm

Exploding dog tissue typically has a force of 100 psi/gram in free space (note that this figure assumes no artificial accellerants, such as gun cotton have been introduced into the dog). And a typical flea (Siphonaptera) weighs .4 mg. Knowing that the force required to accelerate an object weighing .4 mg to a terminal velocity in the range of 10m/s to 100m/s is 890 psi, we can again extrapolate the weight of our host dog with the formula:

W = s * N * (890 / 100)

Where

W = weight in milligrams of host dog.

s = weight of one Siphonaptera (a flea)

N = number of fleas found.

Again, substituting, we have:

W = .4 * 546 * (89 / 100) = 20784 mg

So, we're talking about a dog that weighs about 2 kg, with a surface area of 1310 sq. cm.

I know of only one species of dog that matches the above dimensions, and that is one of those funny looking dogs with the loose, wrinkled skin. In my experience, these dogs are always gray in color, so the answer to Kibo's question, without doubt, is gray.

ALPHA v0.3