# The Tallest Sukkah

In Parshas Emor (Vayikra 23:42) we are commanded to sit in a succah on Succos. A sukkah cannot be more than 20 amahs high and it cannot be lower than 10 tefachim. The opinion of R Avraham Chaim Na’eh is that an amah is 18.9 inches. According to the opinion of the Chazon Ish an amah is 22.7 inches (Frank, The Practical Talmud Dictionary) there are six tefachim to an amah.

What is the tallest possible sukkah to the nearest foot without going over 20 amahs?  Give the answer according to the Chason Ish and of R Avraham Chaim Na’eh .
According to of R Avraham Chaim Na’eh
20 amahs x 18.9 inches = 378 inches = 31.5 feet

Since rounding to 32 feet would be above 20 amahs according to R Avraham Chaim Na’eh we would have to round down to 31 feet.
According to the Chazon Ish
20 amahs x 22.7 inches = 454 inches = 37.8 feet

Since rounding to 38 feet would be above 20 amahs according to Chazon Ish we would have to round down to 37 feet.

What is the shortest possible sukkah in feet to the nearest foot without going under 10 tefachim?  Give the answer according to the Chason Ish and of R Avraham Chaim Na’eh
According to of R Avraham Chaim Na’eh 10 tefach = 1.67 amah
1.67 amahs x 18.9 inches =  31.56 inches = 2.63 feet
We would round up to 3 feet.

According to the Chazon Ish
10 tefach = 1.67 amah
1.67 amahs x 22.7 inches =  37.9 inches = 3.15 feet

Since rounding to 3 feet would be below 10 tefachim according to the Chazon Ish we would have to round up to 4 feet.

Thank you to Pinchas Chernofsky for correcting the issues we had in the original posting of this Torah Math problem!

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