Jack and Nancy, amidst the fascinating world of numbers, stumbled upon a curious riddle adorned with eggs and numerical mysteries.
"In this numerical enigma," Nancy began, "we encounter the perplexing journey of Joan, Tom, and Raoul, who stumbled upon miscounts in curious places."
"Joan's count found itself amiss by just 1 in the 1's place," she continued, "while Tom's count drifted astray by 1 in the 10's place. Raoul, in his endeavor, encountered a deviation by 1 in the 100's place during his count."
"Yet," Nancy added, "amidst this perplexity, the quartet of Sasha, Jose, Peter, and Morris entered the scene, each harmonizing their counts to uncover the elusive truth, arriving at the precise total of 3162 eggs."
"Our journey into the realm of moduli brings us to a pivotal equation," Nancy elucidated, "where the sum 3162, combined with the counts of these three individuals, must align as a multiple of 7."
"In this journey of deduction," Nancy shared, "we uncover the configuration (a, b, c) as (-1, 1, 1), illuminating a path to the answer, revealing that the count of eggs within this intricate puzzle amounts to 439."
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