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Digit Permutations 3 Digit Number Take any 3 digit number, write down all possible numbers that can be made with the three digits, add them up, divide the total by the sum of the 3 digits. Investigate. If All Digits Are Different : - 123 456 789 132 465 798 213 546 879 231 564 897 321 654 987 +312 +645 +978 1332 ? 24=222 3330 ? 15=222 5328 ? 24=222 147 258 369 174 285 396 471 528 639 417 582 693 741 825 936 +714 +852 +963 2664 ? 12=222 3330 ? 15=222 3996 ? 18=222 It seems that when all 3 digits are different the answer to the problem is 222. Can I use Algebra to explain this? abc=100a+10b+c acb=100a+10c+b bac=100b+10a+c bca=100b+10c+a cba=100c+10b+a +cab=100c+10a+b 222a+222b+222c = 222(a+b+c) a+b+c =222 What if 2 of the 3 digits are the same? If 2 digits are the same : - 223 334 566 322 343 656 +232 +433 +665 777 ? 7=111 1110 ? 10=111 1887 ? 17=111 224 559 772 242 595 727 +422 +955 +277 888 ? 8=111 2109 ?19=111 1776 ? 16=111 It seems that when 2 of the 3 digits are the same the answer to the problem is 111. Can...

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