Hello everybody, I hope you have your thinking caps on! I’m back for another Solve it Sunday post, and this week is a tricky one.
As always, answer is in the comments, and you think you have the right answer, make a comment of your own.
During the 19th century, a European colonel in Ethiopia recorded a report of an encounter with local tribesmen, from whom he was purchasing cattle.
He wanted seven beasts, at a cost of 22 birr each. Not being numerate, the herder called a local priest to verify the total price.
When he arrived, the priest dug two parallel columns of holes. The right-hand column represented the purchase price, so in the first hole he placed 22 stones, and then halved the number of stones for each subsequent hole, rounding down. This gave him 22, 11, 5, 2 and 1 stone.
The left-hand column then represented the cattle, and in the first hole he placed seven small stones. He then doubled the number of stones for each subsequent hole in the column, so that the holes contained 7, 14, 28, and 112 stones.
Declaring even values to be evil, the priest then went down to the right-hand column and whenever he encountered an even number of stones – the 22 and 2 holes, in this instance – he removed the stones from that hole and its neighbor in the left-hand column – 14, 28, and 112 respectively – into one pile, which he counted out one by one.
They came to 154 birr, which was indeed 22×7.
Indeed, this technique of multiplication will always work for whole numbers, but why?