My employer has nine workers. The nine of us want to determine what
our average salary is, but none of us wants to divulge his own salary.
Can we find the average without doing so?
source.
Monday, October 19, 2015
499: Blue-Eyed Blondes
If the proportion of blonds among blue-eyed people is greater than among
the population as a whole, is it also true that the proportion of
blue-eyed people among blonds is greater than among the population as a
whole?
source.
source.
498: Circles on a Lattice
On a square lattice, a circle can pass through 2, 3, or 4 points, as in the diagram below. The original question asks for a circle that passes through 5 points, but can you define a circle that passes through other numbers of points? and explain how the circle was created?
source:
On a square lattice, a circle can pass through exactly 2, 3, or 4 points. What about 5? #math #mathchat #MTBoS pic.twitter.com/CsMd6zzbLo
— Matt Enlow (@CmonMattTHINK) August 5, 2015
Sunday, October 11, 2015
495: Pythagorean anti-Triples?
Ask your class if there are any Pythagorean anti-Triples: $\dfrac{1}{a^2} + \dfrac{1}{b^2} = \dfrac{1}{c^2}$ ?
If a, b, c are integers, the question seems harder, since 1/3, 1/4, 1/5 would be (to me) obvious answers - leading to the rules for Pythagorean triples and just using their reciprocals.
Source:
Are there any Pythagorean anti-triples: 1/(a^2) + 1/(b^2) = 1/(c^2) ?
— James Tanton (@jamestanton) October 11, 2015
Saturday, October 10, 2015
494: NetFlix Optimization
An article about the Netflix price hike:
Netflix upped the rate of its “two-screen” plan from $8.99 to $9.99. This plan lets you watch two HD (or regular) streams simultaneously on different devices. Netflix’s “one-screen” and “four-screen” plans remained unaffected.
Here's the thinking: If Netflix subscribers start dropping from the two-screen plans to one-screen plans, this will make them a lot less likely to share their password. No one wants a little offhand altruism to actually affect their viewing habits. That would be bad. If the resulting lack of password-sharers pushes more people to subscribe, then its worth the dollar per subscriber Netflix loses when a user downgrades because of the price increase.
Find the NetFlix subscription numbers to see how the price hike changed things. Was this a good move?
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