A calf-birthing cow puzzle from 1356: how many cows do you have after 20 years?
Start with one cow. Every cow, beginning in her fourth year, gives birth to exactly one new calf each year from then on. No cows die. How many cows are there after 20 years, and what pattern do the yearly totals follow?
Reveal the answer
The count follows the sequence 1, 1, 1, 2, 3, 4, 6, 9, 13, 19, 28... where each term equals the previous term plus the term from three years earlier, giving 1,278 cows by year 20. The 14th-century Indian mathematician Narayana Pandita posed this problem in his 1356 treatise Ganita Kaumudi, producing a sequence now called the Narayana Cows sequence, a lesser-known cousin of the Fibonacci sequence with its own recurrence rule.