The following pair of sentences employ 2 ‘0’s, 2 ‘1’s, 9 ‘2’s, 5 ‘3’s, 5 ‘4’s, 4 ‘5’s, 5 ‘6’s, 2 ‘7’s, 3 ‘8’s and 3 ‘9’s.
The sentences above and below employ 2 ‘0’s, 2 ‘1’s, 8 ‘2’s, 6 ‘3’s, 5 ‘4’s, 6 ‘5’s, 3 ‘6’s, 2 ‘7’s, 2 ‘8’s and 4 ‘9’s.
The previous pair of sentences employ 2 ‘0’s, 2 ‘1’s, 9 ‘2’s, 5 ‘3’s, 4 ‘4’s, 6 ‘5’s, 4 ‘6’s, 2 ‘7’s, 3 ‘8’s and 3 ‘9’s.
(From Lee Sallows and Victor L. Eijkhout, “Co-Descriptive Strings,” Mathematical Gazette 70:451 [March 1986], 1-10.)
Draw a rectangle and pick a point inside it. Now the sum of the squares of the distances from that point to two opposite corners of the rectangle equals the sum to the other two opposite corners.
Above, the red squares have the same total area as the blue ones.
When a building was razed in 1973 on Eldridge Street on Manhattan’s Lower East Side, local resident Adam Purple cleared the lot, gathered manure left by horse-drawn carriages around Central Park, and designed a garden laid out in concentric circles around a central yin-yang symbol. As nearby buildings were torn down he added further circles, until the garden filled 15,000 square feet with corn, cucumbers, cherry tomatoes, asparagus, black raspberries, and strawberries.
The city bulldozed Purple’s lot in 1986, but Richard Reynolds’ London-based blog now documents similar “guerrilla gardening” initiatives around the world.
A problem from the January 1990 issue of Quantum: Forty-one rooks are placed on a 10 × 10 chessboard. Prove that some five of them don’t attack one another. (Two rooks attack one another if they occupy the same row or column.)
Muhammad Didit’s accurately titled video “2 Hours Doing Nothing” has surpassed 5 million views on YouTube.
The (inevitable) mobile game has now been downloaded more than 10,000 times.
One other quick item from Eureka, the journal of the Cambridge University Mathematical Society:
In its 1947 problem drive, the society proposed the following problem:
To find unequal positive integers x, y, z such that
x3 + y3 = z4.
“Although there were some research students in Theory of Numbers among those who tried, not one person succeeded in solving it within the time, yet the solution is extremely simple.” What is it?
In 1918, German flying ace Manfred von Richthofen chased an inexperienced Canadian pilot out of a dogfight and up the Somme valley. It would be the last chase of his life. In this week’s episode of the Futility Closet podcast we’ll describe the last moments of the Red Baron and the enduring controversy over who ended his career.
We’ll also consider some unwanted name changes and puzzle over an embarrassing Oscar speech.
A puzzle by David B., a mathematician at the National Security Agency, from the agency’s May 2017 Puzzle Periodical:
Steve, Tony, and Bruce have a plate of 1,000 cookies to share. They decide to share them in the following way: beginning with Steve, each of them in turn takes as many cookies as he likes (they must take an integer amount, greater than or equal to 1), and then passes the plate clockwise (with Tony sitting to Steve’s left, and Bruce sitting to Tony’s left). Nobody wants to feel like he hogged too many cookies, so they all want to avoid being the player at the end who has taken the most cookies. Additionally, nobody wants to feel cheated by finishing with the fewest cookies. Finally, given that the previous two conditions are definitely met, or definitely cannot be met, each player would like to maximize the number of cookies he eats. The players’ objectives can be summarized as follows:
Objectives:
Objective #1 takes infinite priority over Objective #2. Assuming that all players are perfectly rational, that they are all aware of each other’s rationality and objectives, and that they cannot communicate with each other in any way, how many cookies should Steve take to ensure he meets both objectives and how many cookies will Tony and Bruce take if Steve takes the winning amount?
A raindrop that falls in Erie County, Pa., will travel 2,147 miles to the Gulf of Mexico rather than 15 miles to Lake Erie.
Via MapPorn. River Runner will trace any drop falling in the contiguous United States.
The upper edge of the setting sun is sometimes seen to take on a green tinge, an effect of atmospheric refraction. Normally this is apparent only briefly, but for Richard Byrd’s Antarctic expedition of 1928-1930 it lasted more than half an hour:
Here the sun descends so slowly that it seems to roll along the horizon and as it will be only two days until it is above the horizon all the time for the rest of the summer it clings interminably before, with seeming reluctance, dropping from sight. As its downward movement is so prolonged the last rays shimmer above the barrier edge as it moves eastward, appearing and reappearing from behind the irregularities of the barrier surface. It trembles and pulsates, producing a vibration light of great beauty.
The night the green flash was seen some one ran into the administration building and called, ‘Come out and see the green sun.’
There was a rush for the surface and as eyes turned southward, they saw a tiny but brilliant green spot where the last ray of the upper limb of the sun hung on the skyline. It lasted an appreciable length of time, several seconds at least, and no sooner disappeared than it flashed forth again. Altogether it remained on the horizon with short interruptions for thirty-five minutes.
When it disappeared momentarily it seemed to have been shut off by a tiny spurt, an inequality in the skyline caused by the barrier surface.
“Even by moving the head up a few inches it would disappear and reappear again and after it had finally disappeared from view it could be recaptured by climbing up the first few steps of the [antenna] post.”
(From an account by witness Russell Owen, San Francisco Chronicle, Oct. 23, 1929.)
