Rešitev eksistenčnega problema ▫$G$▫-načrtov z danimi podnačrti je znana za primer, ko je ▫$G$▫ trikotnik s ▫$p = 0, 1$▫, ali ▫$2$▫ disjunktnimi nanj obešenimi povezavami: za ▫$p = 0$▫ sta rešitev ...podala Doyen in Wilson, ki sta prva zastavila takšen problem za Steinerjeve sisteme trojic; za ▫$p = 1$▫ so ustrezni načrti sistemi zmajev, za ▫$p = 2$▫ pa sistemi bikov. Tukaj je dana popolna rešitev problema v preostalem primeru, ko je ▫$G$▫ 3-sonce, tj. graf na šestih vozliščih, sestoječ iz trikotnika s tremi nanj obešenimi povezavami, ki tvorijo 1-faktor.
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