Puzzle 21
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 22
As the auditor for my local theme park, I noticed that on Saturday there were 4,296 children and 2,143 adults and the takings were £98,718.
However, on Sunday, there were 5,146 children and 2,807 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 23
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 24
Tuif cumzye if n fizpye trsg go sre hbw ensl n EOG13 caet eaceyctrd phzmlr paa oe. Rvrrl btuee yegtrr hns brea poavrrgeq go RBT13 aad tue oghrr lrtgees aee lrfg ns tuel jeee. Oug, ybu mny afk, jhnt if ghr cumzye? Wrly, hbw mnnl joedf nrr vn tuif cumzye!
Puzzle Copyright © Kevin Stone
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Hint
This is a simple substitution cipher.
Answer
50.
This puzzle is a simple test to see how easy a ROT13 part encrypted puzzle can be. Every other letter has been converted to ROT13 and the other letters are left as they were. But, you may ask, what is the puzzle? Well, how many words are in this puzzle!
ROT13 replaces each character with the one 13 places away.
A = N, B = O, C = P, D = Q, E = R, F = S, G = T, H = U, I = V, J = W, K = X, L = Y, M = Z, N = A, O = B, P = C, Q = D, R = E, S = F, T = G, U = H, V = I, W = J, X = K, Y = L, Z = M.
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