What is my teacher's favourite animal?

Question

My school teacher, has asked the above question in the spirit of Science Fortnight.

However, he has only left the following on the whiteboard:

Clue 1:

8, 6, 7, 9, 5, 6, 8, 6, 8, 4, _.

Clue 2:

$19 = 21 \times \_ + \frac{1}{2}\times 1 \times \_^2$

(Reverse your answer)

$\times$ represents standard multiplication $\_^2$ is a number to the power of two.

Clue 3:

212, 113, 43, 35, 32, 27, 25, _

What is my teacher's favourite animal?

Hint:

Clue 1 - Chemistry
Clue 2 - Physics
Also - you can solve both of these without any maths. The maths tag was for Clue 3.

Hint 2:

You should get a single number from putting the numbers from each of the clues together in some arrangement. This single number corresponds to an animal.

Answer 1

1. sodium --> 6
2. $s=ut+\frac{1}{2} at^2$ --> T --> 20 reversed 02
3. 23

Reasoning:

1. Seems to be not a known sequence, if related to mathematics something like number of some partial objects of some other objects, if not related to mathematics it can be a number of letters of some other known sequence, first trying with month names, 4th or 5th attempt finished with number of letters in (english) names of chemical elements

2. Replacing numbers with corresponding letters and put the first 2 letters into Google immediattely shows the physical formula as one of first hits - would not be guessed easily as letter v (velocity) is in common use for speed in our country, not u :-)

OP's note: 'u' is in fact the correct letter for this equation, but it is often written as $r = r_0 + v_0t + \frac{1}{2}at^2$ in actual papers, hence the original hint that I was looking for an 'elementary' answer, since $s = ut + \frac{1}{2} at^2$ is used in schools.

3. As suggested and described by P...

"Next number in sequence is 23, considering each term as being 23 written in some base (the blank being base 10)."

OP's note (Putting it all together)

As suggested by Lance M. Peterson:

Clue 1: 6
Clue 2: 02
Clue 3: 23
Formatting this as $6.02 \times 10^{23}$, this is commonly known as Avogadro's constant which is also described as a mole, which is also an animal.

Hence my teacher's favourite animal is:

A mole!

Answer 2

The animal is a mole. Clue 1 - 6 from the number of letters in sodium. Clue 2 - 0.022. Clue 3 - 23 from the fact that the list of numbers are 23 written in a different base, the one we are looking for is base 10,
Avogadros's number is 6.022X10^23.
One mol of anything is just Avogadro's number of that something.

Answer 3

Bat? Hear me out.
Clue 1- The 11th element is Na... na na na na batman. Clue 2 - the variable is t for time. Time backwards is emit. Bats emit sound waves.
> Clue 3- 23. 23rd letter in the alphebet is a w. W looks like an upside down bat

Answer 4

Is it a

Cow?

Reasoning:

Look at clue 3. Next number in sequence is 23, considering each term as being 23 written in some base (the blank being base 10). 23rd letter of the alphabet is 'w'.

Your first clue is not practically solvable without some suggestion as to the method of generation of the sequence. I only got the third one because I noticed the sequence of highest digits was steadily increasing. It isn't a sequence of remainders mod something, since some numbers are odd and some even. The repeated sevens mean it can't be a sequence with a simple generator. The early '9' means it can't be more base shenanigans on top of a simple problem.
Given your comment on the necessity of the 'x1' in the second clue, your assertion that it shouldn't be thought of as a numerical problem and the meaninglessness of 'x' and '_^2' without context, it is also not practically solvable.

You say that the second clue is not necessary for solving the problem. This suggests that the information in the first and second clues is sufficient to solve it. In turn, this suggests that the answer (being the name of an animal) is one that is commonly known, and that each clue gives part of the answer that may be recognizable or that each clue gives the entire answer in a different way. The latter being unlikely, it suggests that the clues each give a letter in a three-letter animal name. Ending with 'w', the obvious answer seems to be 'Cow'.