Google has published a series of problems:
1. A Billboard asking you to find the first 10-digit prime in e. Solving this takes you to a page that asks you to find f(5) where f(1)= 7182818284 f(2)= 8182845904 f(3)= 8747135266 f(4)= 7427466391.
(Hint 0 Hint 1 Mouseover for Answer)
2. A print ad (page0 page1) of a vending machine with 21 input buttons (16, 23, 61, 7, 7, 7, 13, 13, 13, 19, 19, 21, 27, 56, 56, 73, 77, 97, 11, 37, 41 ), choose five to select a good of price (917, 134, 1569, 1649, 1431, 1622, 233, 2094, 1072, 915, 1922, 2437, 2714, 2491, 1886, 2812, 426, 1673, 94, 2139, 2569, 496, 2249, 1553, 1580) where price = V * W + X - Y + Z; {V,W,X,Y,Z} = input buttons. Find the good which is not selectable.
3. A print ad (page0 page1) of a fax machine with extension f(f(extension)) = 1, and access code where f(f(f(code))) = 60097. Find extension and access code if f(x) = 3 * E(x)3 - x and E(x) = number of letters used if x is rendered in American English.
(Hint Mouseover for Answer)

(thanks to Leland for the scans of the print ads)

These problems are trivially brute-forceable, but Google really doesn't want to have a bunch of engineers who solve by brute-force as they have 4B+ pages of online content. So either there's a slick observation-enabled solution, or perhaps these obvious problems are a distraction.

The print ads, in addition to the prominent problem, have a border marking around the problem, labeled "Part A". My conjecture is that since both ads have the "Part A" marking, there is a deep structure to both problems. Identify this, and the border markings will make sense. Solve this problem, and your resume goes to the front of the line at Google.

Last conjecture (for now): the presentation of a problem counts a bunch towards deciding whether it gets worked or not. If you ever teach a class, keep this in mind.

Graph of the Distribution of Spaces between 10-Digit Primes in e Funny that you can find e in e.