# inches and barleycorns

How many barleycorns are there in one inch?

## Problem

Yards, furlongs, inches, cubits, chains and barleycorns are all imperial measures of length.

There are 220 yards in a furlong and 36 inches in a yard. There are 44 cubits in a chain and 54 barleycorns in a cubit. 1 furlong is the same as 10 chains.

How many barleycorns are there in an inch?

*This problem is adapted from the World Mathematics Championships*

## Student Solutions

**Answer:**3

Both of the methods shown use diagrams to organise the information given. There are also good methods which do not use diagrams, but involve similar calculations.

**Working out how many inches and how many barleycorns there are in a furlong**

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$220\times36$ inches = $10\times44\times54$ barleycorns

$1$ inch = $\dfrac{10\times44\times54}{220\times36}=\dfrac{10\times(11\times4)\times(9\times6)}{(11\times2\times10)\times(9\times4)}=3$ barleycorns

**Working in inches using a table**

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$(54\times44)\div(22\times36) = (6\times9\times4\times11) \div (2\times11\times6\times 6)=3$