MATHS WEEK STARTS today and, as is our annual tradition, we’re setting our readers some puzzles. Give them a go!

Day 1: The King of Babylon’s Treasure

Our early ancestors who built Newgrange had to have some mathematical processes to build and orientate the passage tombs over 5,000 years ago. But they left no writings about that so we don’t know what these processes were.

Meanwhile in Mesopotamia, the ancient Sumerians left writing in cuneiform tablets. Their work was recorded as wedge shaped markings in clay tablets. Through these we can discover their mathematics.

Most striking is that the Sumerians used a base 60 or Sexagesimal system. We use base 10, which is handy as we have 10 fingers.

Six tens is 60 so we can also use our fingers in base 60. In fact, a lot of numbers multiply to give 60, that makes 60 useful for making fractions. 60 can be divided by 60 of course and also 30, 20, 15, 12, 10, 6, 5, 4, 3, 2 and 1 giving fractions that could cover a lot of requirements.

This was useful for the Babylonians who needed to reckon land divisions, money and time. This strange system is actually still with us. It is how we count time: 60 seconds in one minute, 60 minutes in one hour.

Here is a puzzle that may involve adding fractions.

The King of Babylon divided a treasure among his Court:

Opening the chest of gold coins, he gave his three chief ministers half the total between them.

Each of his two high priestesses get the same amount as each of the ministers.

The chancellor got half as much as each of the priestesses, and his food taster was left with 10 gold coins. How many gold coins were in the treasure?

This may also be solved by trial and error. Guess a value and see does it work out. If it doesn’t work out, think why? Should you increase of decrease your next estimate?

Come back tomorrow for the answer