Doby is a free elf and he loves socks. On laundry day he sits by his...

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Doby is a free elf and he loves socks. On laundry day he sits by his dresser and randomly conjures two socks (each spell cast brings two socks to him) from his clothesline outside - if they match he folds them neatly and places them into his sock chest, otherwise he returns them to the clothesline (no spell required he walks). He continues this until all of the socks on his clothesline are back in his sock chest. If Doby has 7 pairs of socks drying on his clothesline, how many conjuring spells will he cast on average before all of his socks are back in his sock chest? Doby is a free elf and he loves socks. On laundry day he sits by his dresser and randomly conjures two socks (each spell cast brings two socks to him) from his clothesline outside - if they match he folds them neatly and places them into his sock chest, otherwise he returns them to the clothesline (no spell required he walks). He continues this until all of the socks on his clothesline are back in his sock chest. If Doby has 7 pairs of socks drying on his clothesline, how many conjuring spells will he cast on average before all of his socks are back in his sock chest?