Hints. Solutions at the bottom.
Green Space. I picked this one in order to offer this advice: if no specific measures are given, the solver can designate a simple one. I let the spaces between dots each measure one. The Pythagorean theorem tells us that the “shortcuts” across each corner measure √2.
Watch Your Steps.Draw a segment from the top srtraight down (a perpendicular). To get the triangle’s area we need to discover its base and height. Fill in the side measures you know and then consider the steepnesses on each side. They will give you two different expressions for the top segment of the height and will help you figure the extreme left and right segments of the base.
Arctic Sunrise. The midpoints of each base are the centers from which radii can be drawn to key locations. The Pythagorean theorem will relate two of the radii to the third. The semicircle area formula is one-half of pi times r-squared. Add or subtract the measures of regions to get the blue area.
UB's solutions at the bottoom of this page.
Department of Words
Nothing in Common
# 1-16 in order are gazer, sonic, gazed, lions, raged, loins, graze, coins, grade, coils, range, colds, grain, clods, anger, scold.
Comment: After working over 50 of these puzzles, I think I was lucky in this one to get by with so many anagrams, like colds, clods, and scold. More often anagrams can lead to dead ends because they force you to use the other seven letters over and over. I have been more successful with varying one letter, as in graze to grade to range to freshen the other bunch with a new letter.
Other solutions possible. Send us yours!
Puzzle 1. Processing Puzzle 2. Metropolis
Fit for Four
1. red 2. stay 3. maid 4. stone
5. forward 6. cast 7. bag 8. moustache
Across, in row order: Nemo, mobile, lever; colony, onyx, xenon; before, foreleg, Legos; mono, noodle, levee; sedate, Eden, dense.
Down, in column order: melon, loner, Rover; Fodor, Orono, nomad; pity, type, eddies; renege, gene, never; zero, robot, tense.
Across 1. Beloved (believed – ie + o) 4. Manse (ans. + me) 6. Radar (palindrome)
7. Divided (dividend – N)
Down 1. Bemused (muse + bed) 2. Liner (two definitions, if you follow baseball)
3. Desired (Sir + deed) 5. Ended (fended – f)
The Pythagorean theorem is the key to the diagonals. Adding the two rectangles is adding the central square twice. Apologies: on the right, ignore the 2, it should be 6.
Watch Your Steps.
You all remember rise over run. If not I've rechristened them up and over.
Find the centers of the three semicircles. If we subtract both smaller semis from the largest, we have subtracted 6 too much. The Pythagorean theorem magically erases the square of r3.
© All rights reserved