Random Puzzles 

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 full sequence starts with 3.

Answer
6.

These are the decimal places of π ≈ 3.1415926.

Workings

Hint
The word begins with the letter A.

Answer
Arm.

Double-Checking
swarm army alarm farm warm

Workings

Hint
The 2^nd word begins with the letter B.

Answers
a-a-e = amaze (MZ) --ave = brave (BR) -uie- = quiet (QT) --gon = wagon (WA) p--ot = pivot (IV) vi-e- = vixen (XN) -ac-t = yacht (YH) --met = comet (CO) b--ep = bleep (LE) -u-ge = judge (JD) -lan- = flank (FK) -ra-e = grape (GP) bon-- = bonus (US)
This puzzle isn't guaranteed to have a unique answer, can you find another?