Latest Others Aptitude Question SOLUTION: A 10 digit positive number is said to be a “LearnHub”number if its digits are all distinct and it is a multiple of 11111. How many “LearnHub” numbers are there?

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(#M40011904) OTHERS question A 10 digit positive number is said to be a“LearnHub”number if its digits are alldistinct and it Keep an EYE

A 10 digit positive number is said to be a
“LearnHub”number if its digits are all
distinct and it is a multiple of 11111. How
many “LearnHub” numbers are there?

Asked In Others surajit nag (11 years ago)

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Rituraj  (11 years ago)

10 digit number and all digits distinct
Sum of digits = 45
Number is divisible by 9

Number is divisible by 99999
If number is of form abcdefghij, then

abcde + fghij = 99999
a + f = b + g = c + h = d + i = e + j = 9
We have 5 such pairs (0, 9), (1, 8 ), (2, 7), (3, 6), (4, 5)

So, we can choose abcde in 9*8*6*4*2 = 3456 ways as leading zero is not permitted.
a can have value from 1 to 9 and corresponding value of f is also fixed.
b can have value from balance 8 values ( leaving values fixed for a and f from 0 to 9) and corresponding value of g is also fixed.
..
..
Once abcde is chosen, fghij is automatically chosen

So, 3456 such numbers

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