Ancient Indians used the joints of their fingers to count, a practice still seen today. Each finger has 3 joints, and the thumb is used to count them. How many can you count on one hand? How does this relate to the ancient base-12 counting systems?

Step-by-step solution

Idea: The thumb is the pointer, so only the other four fingers are counted, each with 3 sections. One full round of the hand gives 12, which makes 12 a natural ‘bundle’ size, just as 10 fingers make 10 a bundle size.

1. The thumb does the counting, so it is not counted. That leaves 4 fingers.½ mark
2. Each finger has 3 joints (sections), so one hand counts 4 × 3 = 12.1 mark
3. After 12 you start again on the same hand, so counting happens in bundles of 12. Counting in bundles of 12 is a base-12 system.1 mark
4. Traces of base 12 survive today: a dozen (12), a gross (12 × 12 = 144), 12 hours on a clock face, 12 months. If the other hand keeps track of completed dozens on its 5 fingers, you can count 5 × 12 = 60, which matches the old base-60 counting used for minutes and seconds.½ mark

Answer to write in the exam

Common mistakes that cost marks

• Counting the thumb’s joints too and getting 14 or 15. The thumb is the pointer and is not counted.
• Multiplying 5 × 3 = 15 by treating the thumb as a finger to be counted.
• Answering only the number 12 and not explaining the link with base 12.

How this can come in the exam

Try one yourself

If each hand is counted with finger joints (thumb as pointer), how many can you count using both hands one after the other?

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