what is the answer for stone silver gold and wood riddle alice in wonderland

Alice and her Wonderland are at a crossroads, each step bringing a new riddle. She was passing by the courtroom of the temperamental Queen. Suddenly, she heard an argument between the Queen and king that 64 is similar to 65; she popped out of nowhere and wailed, “Bullshit, if 64 is similar to 65, it will likely be 65 and by no means.”

How Queen presents her argument:

To prove her point, the Furious Queen in question places Alice in front of two chessboards with different prototypes. One with an 8×8 sq. and another with a 5×3 rectangle, then the Queen gives a queue to four unusual service members. They lie to each other, protecting the primary chessboard; Alice notices that two are trapezoids with non-oblique sides measuring 5x5x3, whereas the other two 

are lengthy triangles with non-oblique sides measuring 8 x 3. The Queen exclaims, “You see, that is 64.” 

Then those servicemen again change their position and lie on the second chessboard, which forms 65. Alice is bewildered by the whole arrangement.

What is the answer to the riddle?

Alice moves towards the alignment of the serviceman. It occurs to her that the trapezoid and triangle soldiers look like they cover half of the triangle, and their edges form a diagonal. She realizes that the slopes of the diagonal must be the same. But when she calculates the slope, it appears they’re not the same. 

A trapezoid soldier’s slope goes up two and over 5, making it a slope of 0.4. However, a triangular soldier’s slope goes up three and over 8, making it a slope of 0.375. Before the Queen’s guard could stop her, she drinks her size-reducing potion and jumps over the board to take a closer look. She inquires that there’s a minute area forming a parallelogram that stretches through the entire length of the board. 

There’s not only a loss of a square but also a Fibonacci series where each number is the sum of the two preceding ones. This allows the Queen to form a slope that looks slyly similar.

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