Solutions

The Moon Quiz

1. 365.25 / 29.53 = 12.37 Full Moons per year.

2. The precise times of consecutive Full Moons could conceivably fall in late January and early March. Some term this a Black Moon. A Google search resulted in “No Full Moon in February: About once every 19 years, February does not have a Full Moon. Instead, there are two Full Moons in January and [two in] March, also known as a double Blue Moon. The next Black Moon by this definition will occur in 2037, while the last one was in 2018."

3. Three-fifths of one sixty-fourth is 0.009 or about one percent. I used rounded data. The Audubon Guide reports the Moon mass as 1.23% of Earth's.

4. If we imagine the article’s diagram completed with summer and fall seasons, we can forecast a low 1st quarter Moon in fall, and a summer last quarter phase at moderate elevations.

5. The Moon’s rotation and its revolution are synchronized due to its gravitational interaction with the tides on Earth. More at

https://en.wikipedia.org/wiki/Tidal_locking

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Posers

Words on Target, 2nd Shots

1. WURST    2. ABACI    3. NINNY    4. PINTO    5. from GAFFS to GRADE

Did you find other solutions? Let us know.

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Number Curiosities, Part 1

The Nearness of Them Closest pair: 412 - 365 = 47;

4012-3765 = 247;

50123 - 49876 = 247. Did you find a pattern in selecting the digits?

No Collisions? In the first partition I noticed the triplet of consecutives {3, 4, 5} close to the bottom of the choices. I decided to “look in the mirror” and start with {11, 12, 13} which is just that close to the top. The other mirrored numbers can be found with the formula 16 minus n, for example, 16 – 3 = 13. It worked! The partition is

(1, 8, 15}, {2, 6, 10}, {4, 9, 14}, {3, 5, 7}, and {11, 12, 13}.

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Sums More and Fewer

105 = 52 + 53; it is also the sum of {34, 35, 36}, {19, 20, 21, 22, 23},

{15, 16, 17, 18, 19, 20}, {12, 13, 14, 15, 16, 17, 18},

{6, 7, 8, 9, 10, 11, 12, 13, 14, 15}; and since 105 is triangular

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}.

120 is the sum of {39, 40, 41}, {22, 23, 24, 25, 26}, and

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}.
Numbers with more odd factors are expressible as sums of consecutives in more ways.

32 Skedaddle

{10, 11, 12, 13, 14}has a mean of 12 and a sum of 5 x 12 or 60. Not a power of two.
{15, 16, 17} has a mean of 16 and a sum of 3 x 16 or 48. Also not a power of two.
Any sum of an odd set will have the count of the set as a factor.

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Department of Words

Nothing in Common

# 1-16 in order are: heron, slaty, miner, halts, minor, least, irony, slate, rhino, males, thorn, seamy, north, aisle, horny, malts. N.B. Malts and heron have no letters in common either.

Other solutions possible. Send us yours!

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Five and Ten

Puzzle 1. Apologetic   Puzzle 2. Exhaustion

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Fit for Four

1.  clear   2. feather    3. study    4. post

5. bar   6. secretary    7. catch    8. test

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Crisscross Crunch

Across, in row order: solar, Lara, ravines; lip, popular, area; lapis, Isabel, belay; fever, Erin, in over; mesa, Esau, urcins.

Down, in column order: rosin, inane, newer; bacon, conifer, feral; value, easier, err; pita, tales, Lesotho; Geneva, evade, deans.

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Minicryprtic

Across 1. Dowager (do wager)    4. Civet (I've + CT)    6. Doter (hidden in clue)
7. Medusae (Mede + USA)

Down 1. Decorum (Deco + rum)    2. Waved (Ave + wd)    3. Retiree (2 definitions
5. Tetes (T.S. + ete)

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