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+---- Thread: Puzzler's corner (/showthread.php?tid=1471)
Puzzler's corner - Kaynato - 04-20-2016
It's time to share and solve puzzles with friends.
This means that when you post you should attach at least 5 puzzles, and attempt at least 5 puzzles from previous posts. New puzzles should be numbered accordingly in ascending order, preserving previous puzzles' ordering.
Also - contrary to popular opinion, puzzles 1 and 5 probably have real answers.
Puzzle 1:
Let there be a regular pentagon P with a side length of 20 millimeters, inside which is inscribed a regular star sharing the vertices of the pentagon as its points. The star is shattered into 5 identical kites. The smallest distance from a "trough" of the star to the edge of the pentagon is shortened by 0.02 millimeters. The star is made of element Q, which is identical to gold but when in rectangular strips, varies its dimensions Width and Length as a function of temperature in the relation (Change in Width per second) = (Change in Length per second) = ln((Temperature in Kelvin)/298) + 1. Two kites are deformed into rectangular strips, of the same width as the shorter side of the kite, and dropped from an altitude X. Assuming that the atmosphere is infinite, what is the necessary altitude X to drop the kites from such that the two rectangular strips emit 500 nm light as a result of blackbody radiation when both in series with an ideal voltage source of 100 kilo-Volts?
Puzzle 2:
Five birds are circling overhead. The first one squawks. The second one squawks. The third remains silent. The fourth one yells in a human voice. The fifth one squawks. If it is high noon, and the barn is on fire, what is the chance that the birds are a figment of your imagination?
Puzzle 3:
Is the barn on fire?
Puzzle 4:
A large dog, a tiny dog, and an animate abstract sculpture walk into a bar. The large dog orders a large canister of water. The tiny dog orders a tiny canister of water. What does the abstract sculpture order?
Puzzle 5:
The last three kites from Puzzle 1 are also dropped from the same altitude, but as soon as they reach sea level, they are teleported into the void. In the void, their change in width and change in height is not additive but instead multiplicative. Assuming that they may only dissipate energy via blackbody radiation, when they reach room temperature, how many Indian Rupees may be earned by selling them at the market price of gold in India on January 21, 2015?
RE: Puzzler's corner - a52 - 04-20-2016
1: 500 coulombs/gallon^2
2: trick question: all birds are a figment of the imagination. birds don't exist. they never have.
3: only in universes where the earth is perfectly flat
4: there is as of yet insufficient data for a meaningful answer. indeed, there will never be a meaningful answer to a question like this. the real question is: does it even matter? the eating habits of abstract sculptures may never be properly understand by mere mortals, and indeed, it is enough to know that that the sculpture entered the restaurant.
5: 28199 rupees
RE: Puzzler's corner - Kíeros - 04-20-2016
(04-20-2016, 05:08 PM)Kaynato Wrote: »Puzzle 1:First off, I am going to ignore the geometrical error. It turns out, the distance from the "trough" of a regular pentagram to the pentagon must be 7.2654mm, not 5mm. Other than that, it does seem quite solvable.
Let there be a regular pentagon P with a side length of 20 millimeters, inside which is inscribed a regular star sharing the vertices of the pentagon as its points. The star is shattered into 5 identical kites. The smallest distance from a "trough" of the star to the edge of the pentagon is 5 millimeters. The star is made of element Q, which is identical to gold but when in rectangular strips, varies its dimensions Width and Length as a function of temperature in the relation (Change in Width per second) = (Change in Length per second) = ln((Temperature in Kelvin)/298) + 1. Two kites are deformed into rectangular strips, of the same width as the shorter side of the kite, and dropped from an altitude X. Assuming that the atmosphere is infinite, what is the necessary altitude X to drop the kites from such that the two rectangular strips emit 500 nm light as a result of blackbody radiation when both in series with an ideal voltage source of 100 kilo-Volts?
Regardless of that, each kite has two sides of length 12.360mm and two sides of length 8.981mm. It turns out the toal area is 89.81mm^2, which results in a strip of Q 8.981mm by 10mm.
Skipping forward some, we can calculate that the blackbody temperature needed is 5795K, which leads to a emissivity of 63.95W/mm^2. Since both resistors are the same, the voltage drop in each is 50kV, then the power dissipated across the resistor is 2500000000V^2/R. It turns out, the sheet resistance for gold is about .27 ohms per square, so solving, we can find out the actual size of the sheet needed. This is just solving the equation 63.95(8.981+x)(10+x)=2.5e9/(.27*(10+x)/(8.981+x)), which solves to x=12022.832mm.
From this, we know that the integral from 0 to tf of ln(T(t)/298)+1 dt is equal to 12022.832. We know that gold has a specific heat of .126J/gK, and given the density, leads to a heat capacity of .2235J/K. Then, we know that .2235dT/dt=63.95W/mm^2. Since the expansion is independent of size, for any 1mm portion, .2235dT/dt=63.95W, which has solution dT/dt=286.15W/s, or T=e286.15t. This turns to mean that the growth function is 1.9602dt, and thus, takes 6133.57 seconds. Assuming Earth gravity, this would require a fall distance of .5g(6133.57s)^2, or 184467km.
RE: Puzzler's corner - Reyweld - 04-21-2016
"bread"
Can you figure it out?
RE: Puzzler's corner - a52 - 04-21-2016
"""bread"""
RE: Puzzler's corner - Reyweld - 04-21-2016
Correct!
RE: Puzzler's corner - Kaynato - 04-21-2016
Nice, Kieros! Admittingly, I forgot that I had already set the side length when I set, again, the trough. The fifth problem, comparatively, is much simpler.