Wait! Isn’t this an FQ? Apparently not.
I was watching a game show and my answer was 88 because upside down = horizontal reflection, right? I was wrong. The answer was 96 because their definition of upside down is a 180 degree rotation. Which is correct? 88 or 96?
In the face of ambiguity, both are equally valid. Both being equally valid, the larger number wins.
Once the rules are clarified, for later competitions, then the larger number that fits those rules will win. It wouldn’t retroactively change the earlier result.
Write the number on a piece of paper. Turn the paper upside down, and read the number.
Since when?
Reflection symmetry is distinct from rotational symmetry.
If the word “reflection” was used in the original question, the answer is “88”, using a horizontal line of symmetry.
The answer “96” is correct only if using rotational symmetry, whereby the number is rotated 180°.
In game shows ‘upside down’ applied to a 2 dimensional image means 180° rotation on the Z-axis. Same as in the real world.
- If you turn it upside down it’s the same number. It’s just upside down.
ZZ
It’s 1295 in base 36.
Why stop at base 36? Not sure what the conventions are for higher bases, but I’m pretty sure we can go with lowercase letters, symbols, etc., some of which will be the same upside down.
Show me any physical object which is upside down. It will have been rotated, not reflected.
Yeah - if someone says “you’ve hung this Pollock upside down”, they don’t mean you flipped it horizontally.
nevermind
When I read the question to myself, “96” automatically popped out of my mouth.
When dinosaurs still roamed the earth, my Brownie troop number was 96. We all thought it was so cool to look at the troop number sewn to the top of our sleeves, and the troop number was the same upside down as right side up.
Okay, we were easily entertained. There were only three channels on our black and white TV, phones had cords, and personal computers hadn’t been invented yet.
~VOW
My thoughts, too. For ordinary people with ordinary objects it’s a rotation. A book on a shelf upside down has not been reflected. That would be tricky.
OTOH, for someone like me with all my background in CS and Math, the default mindset on less physical things (and numerals count) is to go with reflection. I even took a course in Transformation Geometry way back when where the basic operations are reflections. (To rotate an object takes 2 reflections. So it is intrinsically more complicated than a reflection.)
FWIW, in my mind “horizontal reflection”, means flipped left-to-right rather than upside down. While “vertical reflection” or “reflection through a horizontal axis” results in upside-down-ness.
Just to introduce additional ambiguity to the terminology.
But that is wrong! (Unless I am missing something obvious?)
Rotations form a cyclic group (generated by a single element), while allowing reflections results in a dihedral group of symmetries, which seems more complicated any way you look at it.