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Intriguing Number Patterns: Deciphering the Mysteries of Numerical Subtraction

Explore the fascinating world of number patterns resulting from subtracting three-digit numbers in a repetitive manner to uncover distinctive sequences. Discover the unique relationships between these numerical operations and witness how they evolve in a captivating mathematical journey. Unveil the secrets behind these systematic deductions and unravel the mysteries hidden within the realm of numeric combinations. Delve into the enigmatic realm of mathematics and witness the mesmerizing transformations that arise from the simple act of subtraction.

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Intriguing Number Patterns: Deciphering the Mysteries of Numerical Subtraction

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  1. 1.心理任想出一個三位數（規定不要 完全相同） 2.將此三位數找出最大、最小的。 3.例如：560最大為650，最小為056。 4.將最大值減去最小值，得到新的三 位數。 5.重複上述動作，三位數會怎樣？

  2. 任意三位數相減 495 • （最大－最小）之值經過有限次將成為。 • abc-cba=(100a+10b+c)-(100c+10b+a) • =100(a-c)+(c-a) • =100(a-c)-(a-c) • =99(a-c)

  3. 981-189=792 [(10×99-9)-(2×99-9)]=8×99 • 972-279=693 [(10×99-18)-(3×99-18)]=7×99 • 963-369=594 [(10×99-27)-(4×99-27)]=6×99 • 954-459=495 [(10×99-36)-(5×99-36)]=5×99

  4. (a-c) • 1 2 3 4 5 6 7 8 9 • 99(a-c) • 99 198 297 396 495 594 693 792 891

  5. 1.推廣上述情形至四位數，會如何？ 2.為何會有如此之現象？

  6. 考慮四位數a,b,c,d 6174 • 經過有限次後將成為6174。 • （且a≧b≧c≧d） • 最大：abcd=1000a+100b+10c+d • 最小：dcba=1000d+100c+10b+a • abcd-dcba= • 1000(a-d)+100(b-c)+10(c-b)+(d-a) • =999(a-d)+90(b-c) • a-d≧b-c

  7. 98 10-0189=9612 • [(9×1000+9×90)-(2×90+9)]=9×999+7×90+ • 9621-1269=8352 • [(9×999+7×90)-(1×999+3×90)]=8×999+4×90 • 8532-2358=6174 • [(8×999+6×90)-(2×999+4×90)]=6×999+2×90 • 7641-1467=6174 (7×999+7×90+18)(1×999+5×90+18)=6×999+2×90

  8. 9441-1449=7992 • 9972-2799=7173 • 7731-1377=6354 • 6543-3456=3087 • 8703-0387=8325 • 8532-2358=6174 • 7641-1467=6174

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