Hint: Does ONE work, does TWO work? How many E's are there already?

Answer: Twelve.

"Cleverly, there are exactly twelve E's in this sentence."

Hint: You can either fix the distance rowed and see what numbers work, or you can fix the number of hours.

Answer: 12 miles.

In the morning, rowing at 2 miles per hour, they rowed for 6 hours. In the afternoon, rowing at 4 miles per hour, they rowed for 3 hours. QED.

There are a number of ways of working this out, and here are two of them:

Method 1
If we assume the distance the rowed upstream to be D miles, we know the morning took (D ÷ 2) hours, and the afternoon took (D ÷ 4) hours, with a difference of 3 hours. So:

  D     D     3
  -  -  -  =
  2     4

Multiplying throughout by 2, and then 4, gives:

  4D - 2D = 24

So:

  2D = 24

And:

  D = 12 miles.

They rowed 12 miles upstream. QED.

Method 2
If we assume they rowed for H hours upstream, we know they travelled H x 2 miles in the morning. In the afternoon they rowed for (H - 3) hours, and travelled (H - 3) x 4 miles. We know these distances are the same, so:

  2H = (H - 3) x 4

Giving:

  2H = 4H - 12

Rearranging gives:

  12 = 2H

So:

  H = 6 hours.

They rowed for 6 hours upstream at 2 miles per hour, which is a total of 12 miles. QED.

Hint: Something is missing from the beginning of the word.

Answer: A headless horseman.

The word HORSEMAN is missing the initial H.

Hint: 2 arrows point to the right, and the others point to the left.

Answer:

Hint: Every word must contain the central letter.

Answer: Astronomy.

Common words:
   ant, ants, art, ASTRONOMY, at, atom, atoms, mast, mat, matron, matrons, mats, moat, moats, most, motor, motors, nasty, not, oat, oats, rant, rants, rat, rats, roast, roost, root, roots, rot, rots, sat, smart, snort, soot, sort, star, stay, stony, storm, stormy, story, stray, sty, tan, tans, tar, tars, to, ton, tons, too, torn, torso, toy, toys, tram, trams, tray, trays, try.

All words:
   amort, ant, ants, antsy, aroynt, aroynts, art, arts, artsy, arty, astony, ASTRONOMY, at, atom, atoms, atomy, atony, mart, marts, mast, mat, matron, matrons, mats, mayst, moat, moats, moot, moots, mort, morts, most, mot, motor, motors, mots, nasty, not, nota, notary, oast, oat, oats, onto, oot, oots, ort, orts, ostomy, rant, rants, rat, rato, ratoon, ratoons, ratos, rats, roast, roost, root, roots, rooty, rot, rota, rotas, roto, rotos, rots, ryot, ryots, santo, sat, satyr, smart, smarty, snoot, snooty, snort, soot, sooty, sort, star, stay, stoa, stoma, stony, storm, stormy, story, stramony, stray, stroma, stroy, sty, ta, tam, tams, tan, tans, tansy, tao, taos, tar, tarn, tarns, taro, taros, tars, tas, to, tom, toman, tomans, toms, ton, tons, tony, too, toom, toon, toons, tor, tora, toras, torn, toro, toros, tors, torso, tory, toy, toyo, toyon, toyons, toyos, toys, tram, trams, trans, transom, tray, trays, trona, tronas, troy, troys, try, tryma, tsar, tyro, tyros.