# What is the largest two-digit number that is the same upside down? **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [June 28, 2024, 4:48pm UTC](https://boards.straightdope.com/t/what-is-the-largest-two-digit-number-that-is-the-same-upside-down/1003450 "2024-06-28T16:48:34Z")\ **Posts on this page:** 16\ **Page:** 1
**Author:** ![Saint\_Cad](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/saint_cad/32/18907_2.png) [@Saint\_Cad](https://boards.straightdope.com/u/Saint_Cad)\ **Post date:** [June 28, 2024, 4:48pm UTC](https://boards.straightdope.com/t/what-is-the-largest-two-digit-number-that-is-the-same-upside-down/1003450/1 "2024-06-28T16:48:34Z")
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? ---
**Author:** ![Sage\_Rat](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sage_rat/32/399_2.png) [@Sage\_Rat](https://boards.straightdope.com/u/Sage_Rat)\ **Post date:** [June 28, 2024, 4:51pm UTC](https://boards.straightdope.com/t/what-is-the-largest-two-digit-number-that-is-the-same-upside-down/1003450/2 "2024-06-28T16:51:01Z")
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. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [June 28, 2024, 4:52pm UTC](https://boards.straightdope.com/t/what-is-the-largest-two-digit-number-that-is-the-same-upside-down/1003450/3 "2024-06-28T16:52:04Z")
Write the number on a piece of paper. Turn the paper upside down, and read the number. ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [June 28, 2024, 5:37pm UTC](https://boards.straightdope.com/t/what-is-the-largest-two-digit-number-that-is-the-same-upside-down/1003450/4 "2024-06-28T17:37:49Z")
> [@Saint\_Cad](#): > > upside down = horizontal reflection, right? Since when? ---
**Author:** ![gnoitall](https://avatars.discourse-cdn.com/v4/letter/g/bb73d2/32.png) [@gnoitall](https://boards.straightdope.com/u/gnoitall)\ **Post date:** [June 28, 2024, 6:15pm UTC](https://boards.straightdope.com/t/what-is-the-largest-two-digit-number-that-is-the-same-upside-down/1003450/5 "2024-06-28T18:15:16Z")
Reflection symmetry is distinct from rotational symmetry. > **[Reflection symmetry](https://en.wikipedia.org/wiki/Reflection_symmetry)** > > In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. > In 2D there is a line/axis of symmetry, in 3D a plane of symmetry. An object or figure which is indistinguishable from its transformed image is called mirror symmetric. In conclusion, a line of symmetry splits the shape in half and those halves should be identical. > I... > **[Rotational symmetry](https://en.wikipedia.org/wiki/Rotational_symmetry)** > > Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation. > Certain geometric objects are partially symmetrical when rotated at certain angles such as squares rotated 90°, however the only geometric objects that are fully rotationally symmetric at any angle are spheres... 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°. ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [June 28, 2024, 6:22pm UTC](https://boards.straightdope.com/t/what-is-the-largest-two-digit-number-that-is-the-same-upside-down/1003450/6 "2024-06-28T18:22:08Z")
In game shows ‘upside down’ applied to a 2 dimensional image means 180° rotation on the Z-axis. Same as in the real world. ---
**Author:** ![Author\_Balk](https://avatars.discourse-cdn.com/v4/letter/a/e0b2c6/32.png) [@Author\_Balk](https://boards.straightdope.com/u/Author_Balk)\ **Post date:** [June 28, 2024, 6:53pm UTC](https://boards.straightdope.com/t/what-is-the-largest-two-digit-number-that-is-the-same-upside-down/1003450/7 "2024-06-28T18:53:11Z")
1. If you turn it upside down it’s the same number. It’s just upside down. ---
**Author:** ![markn\_1](https://avatars.discourse-cdn.com/v4/letter/m/f9ae1b/32.png) [@markn\_1](https://boards.straightdope.com/u/markn_1)\ **Post date:** [June 28, 2024, 7:08pm UTC](https://boards.straightdope.com/t/what-is-the-largest-two-digit-number-that-is-the-same-upside-down/1003450/8 "2024-06-28T19:08:41Z")
ZZ It’s 1295 in base 36. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [June 28, 2024, 7:53pm UTC](https://boards.straightdope.com/t/what-is-the-largest-two-digit-number-that-is-the-same-upside-down/1003450/9 "2024-06-28T19:53:49Z")
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. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [June 28, 2024, 8:21pm UTC](https://boards.straightdope.com/t/what-is-the-largest-two-digit-number-that-is-the-same-upside-down/1003450/10 "2024-06-28T20:21:52Z")
Show me any physical object which is upside down. It will have been rotated, not reflected. ---
**Author:** ![MrDibble](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mrdibble/32/114_2.png) [@MrDibble](https://boards.straightdope.com/u/MrDibble)\ **Post date:** [June 28, 2024, 10:41pm UTC](https://boards.straightdope.com/t/what-is-the-largest-two-digit-number-that-is-the-same-upside-down/1003450/11 "2024-06-28T22:41:18Z")
Yeah - if someone says “you’ve hung this Pollock upside down”, they don’t mean you flipped it horizontally. ---
**Author:** ![GaryM](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/garym/32/241_2.png) [@GaryM](https://boards.straightdope.com/u/GaryM)\ **Post date:** [June 28, 2024, 10:47pm UTC](https://boards.straightdope.com/t/what-is-the-largest-two-digit-number-that-is-the-same-upside-down/1003450/12 "2024-06-28T22:47:59Z")
nevermind ---
**Author:** ![VOW](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/vow/32/3043_2.png) [@VOW](https://boards.straightdope.com/u/VOW)\ **Post date:** [June 29, 2024, 1:52am UTC](https://boards.straightdope.com/t/what-is-the-largest-two-digit-number-that-is-the-same-upside-down/1003450/13 "2024-06-29T01:52:11Z")
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 ---
**Author:** ![ftg](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ftg/32/2801_2.png) [@ftg](https://boards.straightdope.com/u/ftg)\ **Post date:** [June 29, 2024, 1:47pm UTC](https://boards.straightdope.com/t/what-is-the-largest-two-digit-number-that-is-the-same-upside-down/1003450/14 "2024-06-29T13:47:15Z")
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](https://en.wikipedia.org/wiki/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.) ---
**Author:** ![leahcim](https://avatars.discourse-cdn.com/v4/letter/l/b4bc9f/32.png) [@leahcim](https://boards.straightdope.com/u/leahcim)\ **Post date:** [June 30, 2024, 1:19am UTC](https://boards.straightdope.com/t/what-is-the-largest-two-digit-number-that-is-the-same-upside-down/1003450/15 "2024-06-30T01:19:22Z")
> [@Saint\_Cad](#): > > upside down = horizontal 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. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [June 30, 2024, 12:35pm UTC](https://boards.straightdope.com/t/what-is-the-largest-two-digit-number-that-is-the-same-upside-down/1003450/16 "2024-06-30T12:35:23Z")
> [@ftg](#): > > I even took a course in [Transformation Geometry](https://en.wikipedia.org/wiki/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.) 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.