**From New Scientist #2284, 31st March 2001** [link]

Saul Tregenza is a market gardener. He has a field in which he decided that it could be profitable to plant equal rows of daffodils. On a whim prompted by helping with his daughter’s homework, he decided that the number of rows and the number of bulbs in each row should be prime, and that all the digits that would form the two numbers and their product would be different.

Luckily, he found that the field is long enough to hold the maximum possible number of plants under these whimsical conditions.

What was the maximum possible number of bulbs he could plant?

[enigma1128]

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This Python program uses some useful string functions from the

enigma.pylibrary. It runs in 80ms.Solution:The maximum possible number of bulbs is 65,821 (= 7 × 9403).There seem to be remarkably few numbers of bulbs > 10000 that leave us with no repeated digit,

at least when planted in a long narrow strip of 2, 3, 5, or 7 rows.

I found only 17082 = 3 × 5694, 20457 = 3 × 6819, 20754 = 3 × 6918,

21658 = 7 × 3094, 24507 = 3 × 8169, 27504 = 3 × 9168, 28651 = 7 × 4093,

65128 = 7 × 9304, 65821 = 7 × 9403.

Of those, only 4093 and 9403 are prime.

I haven’t yet tested 2 digits times 3 digits.