Random Puzzles 

Workings

Hint
One of the words starts and ends with T.

Answers
eve    = level able   = tablet carve  = scarves as     = ease, hash, sass on     = gong, sons ode    = codec, modem elude  = deluded ape    = lapel ate    = dated, rater rod    = erode

Workings

Hint
Look to the skies for the answer.

Answer
neerg.

These are the colours of the rainbow reversed.

Workings

Hint
Start by labelling the number as ABCDE.

Answer
24,976.

Reasoning
We can start by labelling the digits as ABCDE.

We know that:

(i)  B = 2 x A

and:

     E = A + B

And using (i) we get:

     E = A + (2 x A)
(ii) E = 3 x A

If A = 1, this isn't allowed (as there are no 1's in the puzzle).

If A = 2, then B = 4, and E = 6.

If A = 3, then B = 6, and E = 9, but this isn't allowed (as C has to be the largest digit).

So, A = 2, B = 4, E = 6, and we now have to find C and D.

We also know that:

D = (A + B + C + D + E) ÷ 4

And using (i) and (ii) we get:

D = [A + (2 x A) + C + D + (3 x A)] ÷ 4

so:

3 x D = (6 x A) + C

so:

(iii) D = [(6 x A) + C] ÷ 3

C can only be 7, 8 or 9 (as it's the largest digit, and we've already found 6) and (iii) tells us that it must be a multiple of 3, which means that C = 9. Leaving D = 7.

So the final number is: 24976.

Double-Checking
The answer is 24976.

The fourth digit is a quarter of the total of all of the digits.
   A + B + C + D + E = 2 + 4 + 9 + 7 + 6 = 28, and 28 ÷ 4 = 7.

The second digit is twice the first digit.
   4 = 2 x 2.

The third digit is the largest.
   9 is the largest digit.

The last digit is the sum of the first two digits.
   6 = 2 + 4.

Workings

Hint
The first letters of the words are: T, T, H, D, W, L, H, W, C, N.

Answers
tel + esc + ope = telescope
tim + eta + ble = timetable
hai + rbr + ush = hairbrush
dif + fer + ent = different
wat + erf + all = waterfall
lig + htn + ing = lightning
hea + dli + ght = headlight
whi + rlw + ind = whirlwind
car + til + age = cartilage
new + sag + ent = newsagent