Binaire patronen
Je kunt de drie panmagische 4x4 basisvierkanten splitsen in binaire patronen:
1x getal + 2x getal + 4x getal + 8x getal +1 = panmagisch 4x4
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1x getal + 2x getal + 4x getal + 8x getal +1 = panmagisch 4x4
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1x getal + 2x getal + 4x getal + 8x getal +1 =
panmagisch 4x4
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In totaal zijn er om panmagische 4x4 vierkanten te maken de volgende 4x2 binaire patronen:
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Volg de volgende 3 stappen:
[1] Kies H1a óf H1b en H2a óf H2b en V1a óf V1b en V2a óf V2b (in onderstaand voorbeeld is gekozen voor H1b, H2b, V1b en V2a). In totaal zijn er 2x2x2x2 = 16 mogelijkheden.
[2] Kies als volgorde H1H2V1V2 óf H1H2V2V1 óf H1V1H2V2 óf H1V1V2H2 óf H1V2H2V1 óf H1V2V1H2 óf H2H1V1V2 óf H2H1V2V1 óf H2V1H1V2 óf H2V1V2H1 óf H2V2H1V1 óf H2V2V1H1 óf V1H1H2V2 óf V1H1V2H2 óf V1H2H1V2 óf V1H2V2H1 óf V1V2H1H2 óf V1V2H2H1óf V2H1H2V1 óf V2H1V1H2 óf V2H2H1V1 óf V2H2V1H1 óf V2V1H1H2 óf V2V1H2H1 (in onderstaand voorbeeld is gekozen voor volgorde H1H2V2V1). In totaal zijn er 24 mogelijkheden.
[3] Maak nu het panmagische 4x4 vierkant:
1x getal (H1b) + 2x getal (H2b) + 4x getal (V2a) + 8x getal (V1b) +1 = panmagisch 4x4
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Je kunt hiermee alle 16 (zie stap 1) x 24 (zie stap 2) = 384 panmagische 4x4 vierkanten (inclusief draaiingen en/of spiegelingen) maken !!!
Binaire patronen kunnen worden gebruikt voor grootte (orde) is 2^n (= 2x2, 2x2x2, 2x2x2x2, ...) vanaf 4x4 tot oneindig. Zie uitgewerkt voor 4x4 en 8x8
