Napier's Bones

multiply

48

by

4

In the seventeenth century, John Napier invented a method to perform multiplication using small rectangular pieces of bone labeled with numbers. Select a digit

d

and a number

n

with at most four digits; to multiply them, put the columns with each digit of

n

at the top of the columns after the first. Each column consists of multiples of those top numbers by

d

, with digits placed in the corners of the squares. Go down the first column to the digit

d

. Look at the red rectangle to its right; to get the answer, add the digits between the diagonals as shown by the arrows.