TBT's Tenth Annual Easter Egg Hunt

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Does someone mind sharing the math behind egg 8? I didn't even try it because I can't math and even seeing the answer now I'm like, idk man 😅 I would like to educate myself though!
This was my long-form work for Egg 8 after @FraudulentDimetrodon helped get me unstuck.
gsYjFsY.png

(this was to turn the eggs into variables I could more easily manipulate)

Operators: (reasonably, only plus/minus/multiply can be used)
Ruby = minus (-)
Hopkins = multiply (*)
Cole = plus (+)

Main reasoning is the second equation, d must be a single digit number, and dd a double digit of the same number, which is only able to be obtained by multiplying d by 11 (thus we get d * (b + a) = dd, leaving Ruby as minus by default).

(edited in since I realized I didn't explain this, lol: ) Coco is not a normal operator, but works by inverting the eggs, hence why I've labeled her as "I". Note that this is actually the normal definition for "invert" (i.e. "put upside down"), not the mathematical definition of inversion!

ai = ?
a = ?
b = ?
c = ?
d = ?
e = ?

a - b = c
d * (b + a) = dd -> b + a = 11
e - b = d + c
I(cae) = e(ai)c
I(e*d) + a - e = ??

a must be either 6 or 9 (only numbers that can invert into one another)
c, d, e must be either 0, 1, 2, 5 or 8 (only numbers which can invert into themselves)
b + a, pairs can only be 2 + 9 or 5 + 6. But when trying 9 - 2, c cannot be 7, so we must have a = 6, b = 5, c = 1
We then have e - 5 = d + 1, or e = d + 6. We know d/e must be 0, 2 or 8, and only 2 and 8 make sense, so e = 8, d = 2 to complete that equation.
Inverting a gives us ai = 9.

Therefore, the answer is:
ai = 9
a = 6
b = 5
c = 1
d = 2
e = 8

I(e*d) + a - e = ??
I(8*2) + 6 - 8 = ??
I(16) - 2 = ??
91 - 2 = ??
?? = 89
 
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Logic behind Egg 8.

In calculator digits, 1, 2, 5, 8, & 0 are the only numbers that remain the same when flipped over.
Meanwhile, 6 becomes a different number when flipped, which is 9. So this is the only number that fits the Sky Egg.
3, 4 & 7 all becomes letters so you can't use it.

Ruby is -, while Cole is +, and Hopkins has to be x, because addition & multiplication are closely related operations.
Coco flips the whole number inside the parenthesis because that's the only logical explanation for the set of eggs flipping over completely.
 
Yesterday's three puzzles, eggs 8, 12, and 16, are now closed for submission! And the answers are...

89

Sasha

I3D7H4

Good work, everyone! The eggs for correct answers will be distributed between tonight and tomorrow morning.
nice, I got them all! I knew right away that egg 12 was my lovely bunny boy Sasha :blush:
 
I gave up on 8, I thought it was cute and looked fun but I suck at math and didn't know what numbers to put on the eggs..made my head spin.
For 16, I seriously wondered what was a zipper egg, I saw nothing called a "zipper egg"in the game, so I went with the zipper toy.
 
This was my long-form work for Egg 8 after @FraudulentDimetrodon helped get me unstuck.
gsYjFsY.png

(this was to turn the eggs into variables I could more easily manipulate)

Operators: (reasonably, only plus/minus/multiply can be used)
Ruby = minus (-)
Hopkins = multiply (*)
Cole = plus (+)

Main reasoning is the second equation, d must be a single digit number, and dd a double digit of the same number, which is only able to be obtained by multiplying d by 11 (thus we get d * (b + a) = dd, leaving Ruby as minus by default).

ai = ?
a = ?
b = ?
c = ?
d = ?
e = ?

a - b = c
d * (b + a) = dd -> b + a = 11
e - b = d + c
I(cae) = e(ai)c
I(e*d) + a - e = ??

a must be either 6 or 9 (only numbers that can invert into one another)
c, d, e must be either 0, 1, 2, 5 or 8 (only numbers which can invert into themselves)
b + a, pairs can only be 2 + 9 or 5 + 6. But when trying 9 - 2, c cannot be 7, so we must have a = 6, b = 5, c = 1
We then have e - 5 = d + 1, or e = d + 6. We know d/e must be 0, 2 or 8, and only 2 and 8 make sense, so e = 8, d = 2 to complete that equation.
Inverting a gives us ai = 9.

Therefore, the answer is:
ai = 9
a = 6
b = 5
c = 1
d = 2
e = 8

I(e*d) + a - e = ??
I(8*2) + 6 - 8 = ??
I(16) - 2 = ??
91 - 2 = ??
?? = 89
What in the actual eff yo. Lol I didn’t even try that one, my brain bsploded looking at that nonsense.
 
Only need egg 6 now. I'm tempted to go on a long, long voyage for it. Will be fruitless if I don't find it, however.
 
once again grasping at straws. has anyone ever listened to the bell tree podcast and would that have anything to do with egg 6(66)
 
In calculator digits, 1, 2, 5, 8, & 0 are the only numbers that remain the same when flipped over.
Meanwhile, 6 becomes a different number when flipped, which is 9. So this is the only number that fits the Sky Egg.
3, 4 & 7 all becomes letters so you can't use it.

Ruby is -, while Cole is +, and Hopkins has to be x, because addition & multiplication are closely related operations.
Ugh somehow this stumped me. I totally discounted 6/9 and figured it had to be 2/5 so I couldn’t get the math to work. I thought it just meant 2!=5 but that it had to be a number that could be flipped vertically (around the x-axis and not a rotation) and still be the same. Made it too hard on myself, haha!

ETA: I also considered 0 as a possible digit for a while because it is the same upside down.
Also I thought coco was a square root for a while and I couldn’t figure out a square root of a 3 digit number that became a 3 digit number unless a 0 or decimal was involved which is how 0 got involved in my thinking.
 
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