Solutions

### Posers

Words on Target
Blitz Bank

1. 97+ point words: YUMMY, STORY, PUTTY, WURST, WORST, ZLOTY, and XYSTS – if you know your scrabble dictionary. Did you find others? BUZZY was a surprise. Any that use the letter A?

2. Three for 301: {PUTTY, WURST, ZLOTY}, {ZLOTY, WRYLY, BUZZY}, {YURTS, YUMMY, WURST}, {PUTTY, NUTTY, BUZZY}, {PUTTY, YURTS, PUTTS}.

Lay Back Bank

3. Words that pair to about 180 points: TURNS 92, WORMS 88, WRITS 89, WRIST 89, MUTTS 93, SORTS 91, TRUTH 87, FUSTY 91, GUSTY 92.

Words that pair to around 121: TRAIL 60, SEARS 62, KRAIT 59, PRIME 61, RIGHT 62, RAINS 61, STEAM 58, TRAIN 62, VANES 61.

Did you find other solutions? Let us know.

Number Curiosities, Second Powers

Tasks. The squares of 12, 13, 15, and 18 sum to 862 as do the squares of 11, 14, 16, and 17. The partial product algebra can show that the second, third, fifth, and eighth squares in a consecutive list will sum the same as the first, fourth, sixth, and seventh squares.

Head Scratchers. The squares of 21 through 24 sum to 2030, as do the squares of 25, 26, and 27. The innocent-looking formula (2n^2 + n) will lead you to the first number in the string. For n=3, 2n^2+n=21, and three will be the length of the second string. Let n=4, and use the formula to find consecutive strings of 5 and 4 squares with matching sums.

Double Digit Endings. The square of any multiple of 10 will end in -00. For examples,

30^2 = 900 and 4730^2 = 22,372,900.
A square ending in -44 must be the square of a number ending in 2 or 8. For example,
12^2=144. Can you find other -44 squares? I’ll show what is involved in the search by finding -44 squares stemming from a number ending in -8. Those are represented by 10n+8.

(10n + 8)^2 = (10n + 8)(10n + 8) = 100n^2 + 160n + 64.

The first term in the product will have no impact on the final two digits, but 160n may, and we want it to contribute 80 to the 64 to guarantee a -44 square. We find that if n belongs to the set

{3, 8, 13, 18, 23, …} we get the desired result. If you think there is a pattern here, you’re right.

So squares of (30 + 8), (80 + 8), and (130 + 8) will end in -44. They are 1444, 7744, and 19,044, and so on.

Your turn: Calculate (10n + 2)^2 and find which of these give -44 squares.

### Department of Words

Nothing in Common

# 1-16 in order are: tabor, dinge, labor, eking, bloat, drink, gloat, brink, gated, blink, great, blind, gator, liked, abort, lined.

Other solutions possible. Send us yours!

Five and Ten

Puzzle 1. Worthiness   Puzzle 2. Foreboding

Fit for Four

1. stamp    2. bottle    3. stand    4. squeeze

5. sample   6. pass    7. way    8. kick

Crisscross Crunch

Across, in row order: vivace, cello, Lloyd; pedal, Dalton, Neil; Emperor, Rorem, Max; Annie, Elvis, sun; Aida, Damn, Nia, Amos.

Down, in column order: time, Merman, Anvil; Madame, America, I Can; lento, tootle, Lena; Alone, need, Dinah; lyric, Icarus, Carusos.

Minicryprtic

Across 1. Embargo (Em + bar + go)    4. Pipes (new first letter)    6. Dives (D + Ives)
7. Swindle (sled anagram)

Down 1. Empires (from umpires)   2. Biped (bed + pi)    3. Oversee (O.E. + verse)
5. Saved (two definitions, relief pitcher)