This puzzle is part of the Puzzling Stack Exchange Advent Calendar 2022. The accepted answer to this question will be awarded a bounty worth 50 reputation.
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It was Christmas Eve, and Alice and Bob sat in their armchairs by the fire, determined to stay awake long enough to see Father Christmas come down their chimney. After many hours of keeping their careful vigil, however, their eyelids began to droop and both children nodded off around midnight.
Some time later – though neither could say exactly when – both children were woken by the sound of a grown man sobbing behind the Christmas tree. Rubbing their eyes, they cautiously peered round it. A red suit… a red hat… a white beard… a big sack… Surely, there was only one person it could be! At noticing Alice and Bob awake and staring at him, the man quickly stood up, and their young jaws dropped as he rose to his feet.
Father Christmas – for it was definitely he! – hurriedly wiped his eyes on his sleeve, but stopped upon feeling a gentle tug upon the furry hem of his coat, his rosy face breaking out into a smile as Bob held out a tissue box to him. “Thank you,” he said, gratefully taking a Kleenex. “I very much hope I’m not spoiling your image of me as an always-jolly fellow. It’s just that this Christmas Eve has turned into a particularly stressful one…”
“Oh no,” said Alice. “How come?” Then she paused, afraid she may have just been a little rude. “I mean, feel free to talk to us about it if you wish, Father Christmas. We don’t mean to be nosey, but our parents say it’s always better to talk about problems when we have them, and we’re both very good at listening.”
“Your parents sound very wise,” said Father Christmas, polishing his pince-nez ‘til Bob could see his own face reflected in them. “Perhaps it would be helpful to follow their advice and share my predicament with you…
“You see, my eight reindeer spend so much of the year doing little but feeding and sleeping, that come Christmastime they have energy in great abundance. Really, they ought to be exercised more regularly to keep them sleigh-ready, but I just don’t have the time…
“Anyway, tonight they have been so hyped up that they’ve been pushing themselves to a truly dangerous extent. In fact, on our last take-off just now they really revved themselves up, ran certainly much faster than usual, and launched themselves into the air with such force that I fell backwards from the sleigh, plummeted down towards the ground, and landed – FLOOMF! – on my back, in the snow. Looking up at the sky, I watched them break free from their harnesses, some running this way, some that way, and scattering in all directions. I suppose when I said ‘Dash away! Dash away! Dash away all!’ they took me rather literally this time.”
At this point in the conversation, Bob briefly disappeared to the kitchen, returning shortly afterwards with a tray of tea and biscuits. “Thank you, Bob,” said Father Christmas, accepting a steaming teacup. “I don’t have any idea where to begin searching for them…” Alice put a reassuring hand on Father Christmas’s arm. “Don’t worry,” she said. “I think the good folks at Puzzling Stack Exchange can help you find them.”
Can you?
