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:
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
???
Puzzle 15
Your objective is to place some diagonal mirrors into the grid.
If a ray of light is shone in to the grid from each of the letters, and allowed to bounce off the internal diagonal mirrors, each will exit the grid at the twin of the letter that it entered the grid. For example, a ray entering at either letter D will bounce off some mirrors and exit the grid at the other letter D.
Each row and each column will contain exactly two of the diagonal mirrors.
Hint
How many 1 x 1 squares are there, how many 2 x 2, …?
Answer
2,870 squares.
Reasoning
We have squares sizes from 1 x 1 up to 20 x 20, and these are the counts:
1 x 1 = 400
2 x 2 = 361
3 x 3 = 324
4 x 4 = 289
5 x 5 = 256
6 x 6 = 225
7 x 7 = 196
8 x 8 = 169
9 x 9 = 144
10 x 10 = 121
11 x 11 = 100
12 x 12 = 81
13 x 13 = 64
14 x 14 = 49
15 x 15 = 36
16 x 16 = 25
17 x 17 = 16
18 x 18 = 9
19 x 19 = 4
20 x 20 = 1
