Puzzle 25
Below is a very special grid, around each shaded number are 8 white squares. However, each white square should have a number from 1 to 7. Once filled in, these 8 numbers will sum to the shaded number. In addition, once completed correctly, no row nor column will contain a duplicate number within a white square. For example, the top row may be 5 6 4 2 3 1 7, etc. This is a very difficult puzzle, and many people resort to using a computer to help them.
Puzzle Copyright © Kevin Stone
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Answer
Puzzle 26
As the auditor for my local theme park, I noticed that on Saturday there were 4296 children and 2143 adults and the takings were £98,718.
However, on Sunday, there were 5146 children and 2807 adults and the takings were £122,570.
How much were the children's tickets and adult's tickets?
Puzzle Copyright © Kevin Stone
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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
Puzzle 27
Find two words, which are anagrams of each other, which complete this sentence:
Due to a recent outbreak of a {?} infection in the zebra house, the local animal sanctuary had to {?} their electron microscope correctly, to ensure rapid detection.
Puzzle Copyright © Kevin Stone
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Hint
One word begins with the letter B, and the other begins with the letter C.
Answer
Bacterial and calibrate.
Puzzle 28
In this sequence, which planet would be listed last:
Jupiter Saturn Uranus Neptune Earth Mars ... {?}
Puzzle Copyright © Kevin Stone
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Hint
The answer is something to do with rotation.
Answer
Venus.
The order is based upon the equivalent day of the planet. Jupiter has the shortest day (9.8 Earth hours) and Venus has the longest (243 Earth days).
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