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# Inches and Barleycorns

##### Age 14 to 16 Short Challenge Level:

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  $220\times36$ 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     $(54\times44)\div(22\times36) = (6\times9\times4\times11) \div (2\times11\times6\times 6)=3$

You can find more short problems, arranged by curriculum topic, in our short problems collection.