Solutions

### Posers

Number Curiosities, Third Powers

1. A cube 12 x 12 x 12 has a volume of 1728 (12 x 144) and a surface area of 864 (6 x 144).

2. 35-cubed equals 42,875.

3. The third powers of 1, 2, 3, and 4 sum to 100, the square of the sum of the first powers. The sum of 1 through 5 is 15, and the sum of 1, 8, 27, 64, and 125 is 225 or 15-squared.

4. The sum of the frist n consecutive odd numbers is the square of n. For example, the sum

1 + 3 + 5 + 7 + 9 + 11 = 36

5. The set containing a certain n consecutive odd numbers has a sum of n-cubed. Example: {7, 9, 11} sums to 27. The set of consecutive odds that has a sum of 15-cubed has 15 odd numbers in it. This set begins after we have used 1 + 2 + 3 + ... + 14 of the first odd numbers. The 14th triangular number is 105, and the 105th odd number is 209, so the sum

211 + 213 + 215 + 217 + ... + 239 = 3375 or 15-cubed

### Department of Words

Nothing in Common

# 1-16 in order are: picot, raled, input, cared, point lader, count, plied, court, lined, croup, laten, proud, clean, troup, eland.

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Five and Ten

Puzzle 1. Shattering   Puzzle 2. Absolutely

Fit for Four

1.  false   2. lace    3. skin    4. master

5. trade   6. human    7. call    8. knee

Crisscross Crunch

Across, in row order: winery, year, Ares; renew, Ewan, anodes; stat, attack, knot; tea, Earth, thimble; sedate, Tell, Lloyd.

Down, in column order: Yin, inert, tiered; select, lecture, reap; bylaw, awash, shoer; halo, looks, smile; here, remop, plays.

Minicryprtic

Across 1. Festoon (Cartoon – Cart + Fest)    4. Nodes (anagram)    6. Roped (anagram)
Eritrea (Tired + E. A.)

Down 1. Finagle (fin + eaglet – e – t)    2. Seder (reeds anagram)    3. New idea (anagram)
5. Super (supper – p)