Random Puzzles 

Workings

Hint
Snakes don't have legs.

Answer
6 snakes, along with 7 people and 14 lizards.

Reasoning
We know that for each person (2 legs) there were 2 lizards (4 legs each).

Which means for every person, we can count a total of 10 legs.

Snakes don't have legs, so the total of 70 legs must have been 7 people (and 14 lizards).

This is a total of 21 heads, so the remaining 6 heads were all snakes.

Double-Checking
7 people gives 7 heads and 14 feet.

14 lizards gives 14 heads and 56 feet.

6 snakes gives 6 heads and 0 feet.

For a total of 6 + 7 + 14 = 27 heads, and 0 + 14 + 56 = 70 feet.

Workings

Hint

Answer
385 x 583.

Workings

Hint
There are at least 13 in total.

Answer
There are at least 12 to choose from:

Ape, ewe, cat, kid, doe, fox, ox, kea, nag, ram, pig, cow.

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.