In the realm where numbers dance and sway,
Lies a secret, in Bhaskara’s way.
A six-digit marvel, hidden in plain sight,
A cyclic wonder, a mathematician’s delight.

When multiplied by one to six, in turn,
Its digits dance, twist, and churn.
Yet, behold! No digit dares to flee,
Each permutation, a sight to see.

This number, a riddle wrapped in a guise,
Its sequence, a pattern that mesmerizes.
A tale of numbers that rotate and slide,
In perfect harmony, they coincide.

So, my dear folks, in this numeric ballet,
Can you unveil what the digits convey?
Seek the number, let your mind explore,
In Bhaskara’s footsteps, discover the lore.

Translation

Imagine a number that, when multiplied by 1, 2, 3, …, up to 6, results in permutations of itself. This number has a magical property, akin to the cyclic nature seen in Bhaskaracharya’s work with astronomical cycles and mathematical permutations. Your challenge is to find the smallest 6-digit number that exhibits this cyclic property.

Here’s a hint to get your gears turning: This number, when multiplied by 2, simply rotates one digit to the end, preserving all other digits in their order. This cyclic behavior continues through multiplication by 3, 4, 5, and 6, each time rotating digits in a similar fashion.