Random Puzzles 

Workings

Hint
Look down?

Answer
R.

From the top row of a keyboard – backwards.

Workings

Hint
Another example, PEN is a complete word because:
   -en = ten
   p-n = pin
   pe- = pea

Answer
Two of the words are not complete: bugs, lean.

Reasoning
The remaining 8 words can be changed as follows:
hard:  -ard = card
 h-rd = herd
 ha-d = hand
 har- = harp

port:  -ort = fort
 p-rt = part
 po-t = poet
 por- = pore

duck:  -uck = muck
 d-ck = deck
 du-k = dusk
 duc- = duct

bugs:  -ugs = hugs
 b-gs = bags
 bu-s = buys
 bug- = ---- X

bail:  -ail = hail
 b-il = boil
 ba-l = bawl
 bai- = bait

mast:  -ast = cast
 m-st = most
 ma-t = malt
 mas- = mask

thin:  -hin = shin
 t-in = twin
 th-n = than
 thi- = this

lean:  -ean = mean
 l-an = loan
 le-n = ---- X
 lea- = leaf

fire:  -ire = hire
 f-re = fare
 fi-e = five
 fir- = firm

read:  -ead = bead
 r-ad = road
 re-d = reed
 rea- = real

Workings

Hint
One of the words is waterfall (wat + erf + all).

Answers
som + eth + ing = something
hai + rbr + ush = hairbrush
gra + ssl + and = grassland
pin + eap + ple = pineapple
pol + ice + man = policeman
mea + nwh + ile = meanwhile
wat + erf + all = waterfall
sca + rec + row = scarecrow
yes + ter + day = yesterday
obs + tin + ate = obstinate

Workings

Hint
Try starting with the cube root of the number.

Answer
195 x 197 x 199.

Reasoning
Since we're after three numbers that multiply together, a good place to start is the cube root of 7,644,585, which is roughly 196.99.

Let's try dividing by the closest odd number to 196.99:

   7644585 ÷ 197 = 38805

We're now after whole divisors of 38,805, so trying either odd number either side of 197 might work.

Trying either 195 or 199 gives the answer.

Double-Checking
   195 x 197 x 199 = 7,644,585

Note
Trying the closest odd number to the cube root always works, and the other two numbers are the odd numbers either side.