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

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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.

Other solutions possible. Send us yours!

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Five and Ten

Puzzle 1. Shattering   Puzzle 2. Absolutely

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Fit for Four

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

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

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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.

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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)

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