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

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.

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}.

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.

{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.

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!

Five and Ten

Puzzle 1. Apologetic   Puzzle 2. Exhaustion

Fit for Four

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

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

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.

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)