Random Puzzles 

Workings

Hint
Start with the possible answers where the first digit is a prime number, and then look at the third digit.

Answer
23,475.

Reasoning
By (1), the first digit is prime:
   2----
   3----
   5----
   7----

By (3), the third digit is twice the first digit, so we can eliminate 5---- and 7----:
   2-4--
   3-6--

By (4), the fourth digit is the third digit plus three:
   2-47-
   3-69-

By (5) the fifth digit is the difference between the first digit and the fourth digit:
   2-475
   3-696

We know from the introduction that no digit is repeated, so we can eliminate 3-696. And, by (2) the second digit is the fifth digit minus the first digit:
   23475

Workings

Hint
This question involves the months of the year in some way.

Answer
4 3 1.

Reasoning
This is the sequence of the length of the name of the month, and the number of days in that month.

7 3 1 = January, which has 7 letters, and 31 days.

8 2 8 = February, which has 8 letters, and 28 days.

5 3 1 = March, which has 5 letters, and 31 days.

5 3 0 = April, which has 5 letters, and 30 days.

3 3 1 = May, which has 3 letters, and 31 days.

4 3 0 = June, which has 4 letters, and 30 days.

Which means the next three digits are:

4 3 1 = July, which has 4 letters, and 31 days.

Workings

Hints
The first letters of the words are: B, S, E, W, E, L, P, C.

Answers
Any animal that fits is correct, but these are possible answers:
fahjec   = badger, barbet, gannet, marten qsaxe    = crane, skate, snake, whale eep      = eel zoth     = fowl, lory, moth, pony, wolf, worm epessawx = elephant feyuv    = lemur, xerus zowqud   = possum pol      = cod, cow, dog, fox, hog

Workings

Hint
If we look at all of the clues, each person appears exactly twice.

Answer
Alex had been teaching for 21 years.
Billie had been teaching for 15 years.
Charlie had been teaching for 7 years.

Reasoning
If we look at all of the clues, each person appears exactly twice.

So the total of the three clues gives us two lots of Alex + Billie + Charlie = 36 + 22 + 28 = 86.

So, Alex + Billie + Charlie = 43 years.

In each clue we are given two of the people, so we can use this to find the missing person:

   Charlie and Billie had been teaching for a total of 22 years, which means that Alex must be: 43 − 22 = 21 years.

   Charlie and Alex had been teaching for a total of 28 years, which means that Billie must be: 43 − 28 = 15 years.

   Alex and Billie had been teaching for a total of 36 years, which means that Charlie must be: 43 − 36 = 7 years.

Reasoning With Algebra
Let Alex = A, Billie = B and Charlie = C, then:

[1]   A + B = 36
[2]   C + B = 22
[3]   C + A = 28

If we use [3] − [2] we have:

[4]   A − B = 6

If we use [1] + [4] we have:

   2A = 42
    A = 21

By [1] B = 15. By [3] C = 7.