Random Puzzles 

Workings

Hint
I bought at least 8 of each stamp.

Answer
Eight lots of 11p, 17p and 21p, and nine lots of 3p and 9p.

Reasoning
For three denominations of stamp I was asked to buy 8 of each, and for the other two denominations I had to buy 9 of each.

So I had to buy at least 8 of all five denominations.

This would be for a total of 8 x (3 + 9 + 11 + 17 + 21) = 488p = £4.88.

The remaining 12p has to buy the remaining 2 stamps, which must have been 3p and 9p.

Double-Checking
9 x 3 = 27
9 x 9 = 81
8 x 11 = 88
8 x 17 = 136
8 x 21 = 168

For a total of 27 + 81 + 88 + 136 + 168 = 500p = £5.

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
Look closely at the beginnings and the ends of the words.

Answer
Ice.

Each word begins with the last two letters of the previous word.

Workings

Hint
There are 60 seconds in a minute, and 60 minutes in an hour.

Answer
Seconds in a week.

Reasoning
There are 60 x 60 x 24 x 7 = 604,800 seconds in a week.

There are 60 x 24 x 365 = 525,600 minutes in a (non-leap) year.