Balanced Ternary

A red and blue scale with 4 purple blocks on one side and coloured weights on the other.
A black, yellow, white and purple exhibit sitting in a white room. On the exhibit table sits a blue and red scale.

The ternary counting system is based on 'threes', while our traditional decimal counting system is based on 'tens'.

How it works

Work out the mass of an unknown object by comparing it to a series of known masses ( 50 g, 150 g, 450 g and 1350 g) using a novel counting system known as balanced ternary.

Things to try or ask around the exhibit

  • What numerical pattern can you pick up in the known masses 50 g, 150 g, 450 g and 1350 g?
  • What's the smallest number of masses you can use to make the unknown object balance?
  • If you count to 100, what base number is that counting system based on?

Background

This exhibit combines problem solving with a model of the ternary counting system.

Numbers are commonly represented using a system called base ten. You break a number into groups of ten, and count how many ones, tens, hundreds (tens of ten), thousands (tens of hundreds) and so on. For example, 121 is shorthand for 100 + 20 + 1 or (1×102) + (2×101) + (1×100).

In base three, called ternary, you break numbers into groups of three. You count how many ones, threes, nines (threes of three), twenty-sevens (threes of nines). For example, 121 in base three is shorthand for (1×32) + (2×31) + (1×30) = 16.