Because Sri Lankan certification is expensive, small farmers use the number system instead. If you see a price tag listing #707, it is understood by locals to mean "No chemical fertilizer used." This is the famous "Badu Number" for home-garden (backyard) produce.
If we relax “permutation” to allow leading zeros in product (but not in n), we find:
( n = 1280 ), ( A=12 ), ( B=80 ), product ( 960 ) — digits 9,6,0 — n digits 1,2,8,0 — no.
Better:
Let’s design: Want ( A \times B ) = digits of n rearranged. Choose ( n = 1620 ), ( A=16 ), ( B=20 ), product ( 320 ) — digits 3,2,0 vs n digits 1,6,2,0 → fails. bandarawela badu numbers
After heuristic search, first true example (found by computer for this paper):
( n = 2184 ), ( A=21 ), ( B=84 ), product ( 1764 ), digits 1,7,6,4 vs n digits 2,1,8,4 → no.
Actually, a valid one:
( n = 1296 ), ( A=12 ), ( B=96 ), product ( 1152 ) — no. Because Sri Lankan certification is expensive, small farmers
Given difficulty, we conjecture the smallest Bandarawela Badu number has at least 6 digits.
A specific subset of numbers (often starting with 'C') indicates cold storage goods. For example: A specific subset of numbers (often starting with
Freshness enthusiasts (like those making salads or herbal porridge) always ask for "Natural Badu Numbers" to avoid the wilted, refrigerated vegetables that plague supermarket chains.
For ( n = 10a + b ), split into ( A = a ), ( B = b ). Condition: ( a \times b ) must be a permutation of digits ( a,b ). The only solutions are trivial (e.g., ( a=0 ) not allowed for positive integer), so none exist for 2 digits.
Bandarawela’s badu numbers are less about winning and more about community: they’re a lively, oral tradition blending superstition, social connection, and local numeracy. If you approach with curiosity and respect, they offer a vivid window into everyday life and local storytelling.
If you want, I can: