Roble number II
A roble number is a positive integer that does not contain any of the digits 1, 4, and 3. The first few roble numbers are 2, 5, 6, 7, 8, 9, 20, 22, 25.... How many roble numbers are there between 987 and 5678?
Related Problems: You might also want to try Roble Problem I and Roble Problem III .
The answer is 532.
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1 solution
"The roble number is a base-7 number system with 0 r → 0 7 , 2 r → 1 7 , 5 r → 2 7 , 6 r → 3 7 , 7 r → 4 7 , 8 r → 5 7 , and 9 r → 6 7 ."
(This sentence is from @Chew-Seong Cheong 's solution of Roble Problem I )
So 9 8 7 r = 6 5 4 7 = 3 3 3 1 0 , 5 6 7 8 r = 2 3 4 5 7 = 8 6 6 1 0 ,so there are 8 6 6 − 3 3 3 − 1 = 5 3 2 (the − 1 is because it's exclusive)