Intellectual’s first approach to the problem was a mathematical one.

He counted the strange flowers and found that there were 13 of them.

“(Mean, mean 13!)” Imaginational muttered.

And furthermore, if they were grouped suitably, he could see groups or lines of the prime numbers and Fibonacci numbers up to 13. He put red ribbons joining the flowers to show what he meant.

“But they are not perfectly lined up to show both of those” interrupted Parfait “you have to move the one with the blue butterfly on it into the line of six to make the 7 for the prime numbers but then you would not have the prime number 11 you get when you add the line of six and the line of five”

“Picky, picky!” grumbled Intellectual. But he had to concede that Parfait was correct and therefore the puzzle was probably not related to prime numbers.

It did not help that Intellectual was not sure what he WAS trying to prove.

He wondered whether the arrangement of the flowers was a code of some kind

He visited the Codes for Kids page on The Republic of Mathematics blog to search for clues

http://www.blog.republicofmath.com/codes-for-kids-1-simple-substitution-ciphers

Then he decided that he would be able to solve the puzzle by solving the simultaneous equations for the two lines of flowers and produced this

The answer must be 42

(because the answer to everything is 42

eg How many swans-a-swimming and geese-a-laying had the true love received by the 12^{th} day of Christmas?)

There are 13 flowers

Therefore

13x = 42

Therefore

x = 3

(And that is correct because there are 3 flowers separate from the lines which form a triangle when you join them)

Now

5x + a = 42

And

6x + b = 42

(Because the answer is always 42)

Therefore

15 + a = 42

a = 27

And

18 + b = 42

b = 24

“What is that supposed to prove?” asked Parfait.

“I don’t know. But it is VERY INTERESTING and deeply significant!” claimed Intellectual

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I see the doogies are displaying their OCD tendencies! My head is spinning! Maybe they are taking this a bit too seriously?