The Cowherd at the Gates
A folk puzzle from Karnataka: cows passing equally through gates.
Click to zoom
Equal lines through 3 gates, then 5, then 7: the number of cows must be a multiple of all three.
Find when repeating patterns line up, how many cows the cowherd had, and how many children were playing Fire in the Mountain.
Preview · progress not saved — Chapter 1 is free
A pattern that repeats every 6 and one that repeats every 4 line up every LCM(6, 4).
If one thing repeats every steps and another every steps, then once they line up, they line up again after LCM(, ) steps.
Two rows of coloured stars with different repeat lengths.
Problem. In the two rows, the colours repeat. When will the blue stars meet next? (Textbook p. 63, Q1)
Repeating-pattern and smallest-multiple questions.
At which star do the blue stars meet after star 4?
First find the common multiples, then pick the one that fits the extra rule.
A folk puzzle from Karnataka: cows passing equally through gates.
Equal lines through 3 gates, then 5, then 7: the number of cows must be a multiple of all three.
Equal groups through 3, 5 and 7 gates, and fewer than 200 cows.
Problem. A cowherd with fewer than 200 cows reaches crossings with 3, 5 and 7 gates. Each time, an equal number of cows passes through each gate. How many cows does he have? (Textbook p. 63, Q5, from the folklore mathematics of Karnataka)
The circle game where children form groups of the number called.
When a number is called, everyone forms groups of that size. Anyone left over is out.