<Text-field style="Heading 1" layout="Heading 1"><Font family="Arial">Starting simple: Assume a widthless sofa!</Font></Text-field>

Let's start with the simpler problem by assuming the sofa has zero width. The general case will follow easily.

Idea: Compute the shortest gap that the sofa has to pass through as it makes the turn. That is, minimize LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRJyYjOTUyO0YnL0YwUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0Y/Rj9GPw== with respect to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIi5GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSS1GNjYtUSJ+RidGMkY5RjtGPUY/RkFGQ0ZFRkdGSkZMRjI=

If we're lucky, the sofa will be longer than this gap, and we won't have to move anything.

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JEYrLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0YrRjE=

Let h be the width of the hallway and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRKCZ0aGV0YTtGJy9GMFEmZmFsc2VGJy9GM1Enbm9ybWFsRidGP0Y/LUYsNiNRIUYnLUYjNiRGQUY/RkFGPw== be the length of the line segment that just grazes the corner and touches both outer walls at an angle of \316\270 with the inner wall. We first need to find the angle at whichLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRJyYjOTUyO0YnL0YwUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0Y/Rj9GPw== is minimum. (Intuition demands that 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, but rigor demands we prove it formally, which we do here.)

We have

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

Zio2I0kmdGhldGFHNiJGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwmKiZJImhHRiUiIiItSSRzaW5HRiVGIyEiIkYsKiZGK0YsLUkkY29zR0YlRiNGL0YsRiVGJUYl

We solve 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 for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIi5GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSUYy

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIidGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdRJjAuMGVtRictSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYlUScmIzk1MjtGJy9GMEY9RjkvJStleGVjdXRhYmxlR0Y9RjlGOUZZRjk=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCYqKEkiaEc2IiIiIiktSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2I0kmdGhldGFHRiUiIiMhIiItSSRjb3NHRipGLUYmRjAqKEYkRiYpRjFGL0YwRihGJkYm

LUkmbW92ZXJHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JS1JI21vR0YkNi5RIj1GJy8lMGZvbnRfc3R5bGVfbmFtZUdRKDJEfk1hdGhGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdGNy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjcvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGRi1JJm10ZXh0R0YkNiVRK35zaW1wbGlmeX5GJ0YvRjIvJSdhY2NlbnRHRjc=

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JSFH

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As with any 3rd degree equation, this one has three solutions.

It looks like we want the real solution, 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. Our intuition was right!

This means the smallest gap we have to squeeze through is the one formed when the sofa is at an angle of 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 the wall. How big is this gap in terms of h?

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print(); # input placeholder

LCQqKCIiIyIiIkkiaEc2IkYlKUYkI0YlRiRGJUYl

LUkmbW92ZXJHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JS1JI21vR0YkNjFRJyZyYXJyO0YnLyUlc2l6ZUdRIzE0RicvJSVib2xkR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EoMkR+TWF0aEYnLyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y6LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y/LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGPy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRk4tSSZtdGV4dEdGJDYoUSxhdH41fmRpZ2l0c0YnRi9GMkY1RjhGOy8lJ2FjY2VudEdGPw==

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LCQqJiQiJiVHRyEiJSIiIkkiaEc2IkYnRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

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Punch Line:

A zero-width sofa whose length is less than 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will make the corner. (We'll see how to account for the width of the sofa presently.)

Let's visualize this result when h = 1.5.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JEYrLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0YrRjE=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJyYjOTUyO0YnL0YwUSZmYWxzZUYnL0YzUSdub3JtYWxGJy8lK2V4ZWN1dGFibGVHRj5GP0Y/RkFGPw==

LCYqJkkiaEc2IiIiIi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjSSZ0aGV0YUdGJSEiIkYmKiZGJEYmLUkkY29zR0YpRixGLkYm

print(); # input placeholder

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<Text-field style="Heading 1" layout="Heading 1"><Font family="Arial">Accounting for the sofa's width</Font></Text-field>

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Now for the almost incredibly simple result:

If the sofa's length plus double its width is less than 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, the sofa will make the turn!

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