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
Is there a missing letter?

Answer
The entire conundrum does not have the letter E.

However, it does contain every other letter.

Workings

Hint
The word MARCH appears 46 times.

Answer
The word MARCH appears 46 times.

Workings

Hint
Try finding the cube root of 190,747.

Answer
53, 59, and 61.

Reasoning
Start by taking the cube root of 190,747, which is approximately 57.56.

The next highest prime number is 59:

   190,747 ÷ 59 = 3,233

Let's try the next prime number, which is 61:

     3,233 ÷ 61 = 53

53, 59, and 61, are all prime, and are consecutive, so this is the answer.

Double-Checking
   53 x 59 x 61 = 190,747