Brain Teasers and Puzzles 

Workings

Hint
Think of Roman numerals.

Answer
Delta.

Take the Roman numerals in sequence, and convert to the phonetic alphabet.
  1 = I = India
  5 = V = Victor
 10 = X = X-Ray
 50 = L = Lima
100 = C = Charlie
500 = D = Delta

Workings

Hint
In the first box, look at 7 & 3, and 4 & 1, to see how we can use them to make 12.

Answer
4.

Reasoning
For each row, the left minus the right gives a number.

The numbers for the rows are then multiplied together.

In the first box:

   7 – 3 = 4
   4 – 1 = 3

so 4 x 3 = 12

In the second box:

   9 – 2 = 7
   8 – 3 = 5

so 7 x 5 = 35

In the last box:

   6 – 2 = 4
   8 – 7 = 1

so 4 x 1 = 4.

Workings

Hint
The missing word is in these locations: lo---e, ---ch, s---he, ---er, va---e.

Answer
Cat.
loe  = locate ch   = catch she  = scathe er   = cater vae  = vacate

Workings

Hint
This is quite a tricky puzzle, and knowledge of algebra would certainly help.

Answer
The children tickets were £14, and the adult tickets were £18.

Reasoning
There are a number of methods for solving this problem, including:

Using a spreadsheet. Using a computer program. Using the intersection of lines on a graph. Using an online equation solver. Solving simultaneous equations using algebra. Solving simultaneous equations using inverse matrices.
Here is my solution using simultaneous equations and algebra.

First construct two algebraic equations, where 'c' is the number of children, and 'a' is the number of adults:

[1]   4296c + 2143a = 98718
[2]   5146c + 2807a = 122570

To make the number in front of 'c' the same on both, we multiply [1] by 5146 and [2] by 4296 to give:

[3]   22107216c + 11027878a = 508002828
[4]   22107216c + 12058872a = 526560720

Now we can do [4] – [3] to give:

   1030994a = 18557892

Divide throughout by 1030994 so that:

   a = 18

Substituting a = 18 in [1] will give:

   4296c + 2143 x 18 = 98718
   4296c + 38574     = 98718
   4296c             = 60144
       c             = 14

Double-Checking
c = 14 and a = 18

4,296 x 14 + 2,143 x 18 = 98,718

and

5,146 x 14 + 2,807 x 18 = 122,570