Kakuko with Izanagi Wahishiti
To solve Kakuko (the puzzle traditionally given to lovelorn, broken-down geisha in mid-18th century Western Japan) you must fill in the squares of the central circle using numbers which are multiples of their neighbours' cube roots.
The outer circle of squares must only contain numbers which are multiples of the square roots of the values obtained by dividing these numbers by the original values of the numbers in the immediately diagonal squares of the inner circle.
Clues are obtained by cross referencing the numbers given in the black-bordered squares with the symbols arrayed across the 'dragon's back' base row.
When Kakuko is completed (known in the tradition as 'liberation moment'), the sum of the solved squares must be zero. The example provided is a facsimile of that given the elderly geisha Yozi-Wawa by the judge and epicure Hei-Tei San in 1765. It is said that Yozi-Wawa solved the puzzle within 3 days, and when she presented it to him, the judge became enlightened upon gazing at the numbers on the riti parchment, and entered a zen monastery, where he became famous for inventing the koan 'does the carp sing?'
The legendary samurai Odanananaga Onaraganananaga said 'Nothing tests the mettle of my soul so much as Kakuko and an unruly geisha.'
May you benefit from this gift of Kakuko, 'the problem that ventilates the soul as it strangles the ego' (Kazi Kadiki Do, 5th century Kakuko Master).
