by Mark Valentine

#### Published Sunday April 09 2023 (link)

The new King’s currency has 64 Minims (circular coins) per Suttas (notes). Each coin’s value is proportional to its face area, and is a whole number of cm in diameter, starting with 1 cm for 1 Minim.

The King only wanted denominations such that his citizens can pay any amount below 1 Suttas using no more than a certain number of coins for the transaction. This number is the smallest possible, given the above conditions. His mint suggested that if just two values could require an extra coin, they could reduce the number of denominations needed. The King agreed and placed one of each minted denomination flat and face up in a rectangular display, with each coin’s edge resting along the display’s base. The order of the coins minimised the width of the display, with the smallest coin to the right of the centre.

What are the diameters in cm, from left to right?

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I needed to see Jim’s solution to understand the puzzle.
My program doesn’t support multiple adjacent coins which can be minimized (the diameters don’t differ enough for this)

A simpler formula for r (in miminize function) is (a * b) / (sqrt(a) + sqrt(b))^2

While my intermediate results are the same as Brians my final dsiplay line-up is different. I can’t figure out why. Any ideas?

Hi John, your width variable ndw is sometimes too small. In your final solution the 4th coin may not be considered in the width as it fits in the gap between the 3rd and 5th coin (without adding to the total width). I have written a minimize function for such cases.

For a picture see: