Question

Let the sum of all numbers greater than 10000 formed by using the digits 0, 1, 2, 4, 5 & no digit being repeated in any number be $k$.Let the sum of digits of k be m.Find $m/6$ ?

Answer 1

We have $5$ digits.

It shall be greater than $10,000$ which is always true for our case.

So, starting from $1$ we have different cases similarly for any other digit.

Total numbers $=4\times 4\times 3\times 2$

$=96$

With $1,2,4,5$ as 1st digit we have $24$ numbers each.

Sum of all numbers in unit place $24\times (0+1+2+4+5)$

$=288$

Sum of all $5$ digit numbers $=288(1+10+100+1000+10000)$

$=288\times 11111$

$=3,199,968$

However, some will start with $0$ so all $4$ digit numbers sum $=6\times (1+2+4+5)(1+10+100+1000)$

$=79992$

Total sum $=3,199,968-79992$

$=3119976$

Sum of digits $=36$

$\Rightarrow K/6=6.$

Hence, the answer is $6.$