Question 820215: All six digit numbers that can be formed using the digits 2 3 5 6 7 and 9 are written. If each digit can be used only once what is the largest of these numbers that is divisible by 11.
I tried using the divisibility rule off 11 but none of the combinations are working.
Answer by solver91311(24713)   (Show Source):
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The largest 6 digit number that can be created using the digits 2, 3, 5, 6, 7, and 9 without repetition is:
976532
The next is
976523 (swapped positions of the 3 and the 2)
followed by
976352 (swapped positions of the 5 and the 3)
976325 (left the 3 in the 100s position and swapped 5 with 2)
976253 (put the 2 in the 100s posit and the 5 in the 10s posit)
976235 (swapped the 5 and 3 from above -- all possibilities of the low three digits accounted for)
975632 (from the original number, swap 5 and 6)
(from here, make all possibilities of the new low three digits -- if you need to go that far)
Apply the divisibility rule to these. If none of them work, continue the pattern creating the next largest number and applying the divisibility rule for 11. The first one you find is the largest that is divisible by 11.
John
My calculator said it, I believe it, that settles it
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