Random Puzzles 

Workings

Hint
The first letters of the words are: N, C, C, C, E, H, O, C, L, M.

Answers
new + sag + ent = newsagent
cro + cod + ile = crocodile
col + lis + ion = collision
cla + ssr + oom = classroom
enc + our + age = encourage
hai + rbr + ush = hairbrush
oth + erw + ise = otherwise
clo + sen + ess = closeness
lig + htn + ing = lightning
mar + gar + ine = margarine

Workings

Hint
Look at Digit 3 first.

Answer
6394.

Reasoning
Labelling the clues:

Digit 2 is smaller than Digit 4 Digit 4 is two thirds of Digit 1 Digit 1 is two thirds of Digit 3 Digit 3 is three times Digit 2
By (3), Digit 3 is divisible by 3:

   Digit 3 = 3, 6, 9

By (3), Digit 1 is two thirds of Digit 3:

   Digit 1 = 2, 4, 6.

But, by (2), Digit 1 is divisible by 3:

   Digit 1 = 6, and Digit 3 = 9.

By (4), Digit 3 is three times Digit 2:

   Digit 2 = 3.

By (2), Digit 4 is two thirds of Digit 1:

   Digit 4 = 4.

Workings

Hint
Start by filling the 7 gallon container.

Answer
Here are the contents of the containers after each stage:
A  B
0  7    fill B
3  4    fill A from B
0  4    empty A
3  1    fill A from B
0  1    empty A
1  0    fill A from B
1  7    fill B
3  5    fill A from B

This leaves 5 gallons in container B after 8 steps.

Workings

Hint
Which letters are missing?

Answer
The letter was written on a typewriter that has a problem with the top row of letters printing correctly. The letter should have read:

Dear Kevin,

I would like to complain about the top row of my typewriter.

These letters do not appear to be working correctly.

As you can see, they are missing from this document.

I would be very grateful if you could correct this problem immediately.

Kind regards.

Sam South.