Random Puzzles 

Workings

Hint
I bought at least 5 of every stamp.

Answer
Five lots of 2p, 7p and 15p, and six lots of 10p, and 20p.

Reasoning
The shopkeeper rightly figured that I required five lots of all of the stamps, which came to (2p + 7p + 10p + 15p + 20p) x 5 = £2.70.

For two of the stamps I needed one more of each, and these must have added to the remaining 30p, so can only have been the 10p and 20p stamps.

Workings

Hint
Try converting each number to a letter.

Answer
19.

From the alphabetical position of S, making the word PUZZLES.
16 = P
21 = U
26 = Z
26 = Z
12 = L
 5 = E
19 = S

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.

Workings

Hint
The first word is ONE.

Answer
One good turn deserves another.