I look at it this way:
-- There are 90,000 numbers with five digits. (100,000 minus 10,000 with less than 5 digits)
-- If the sum of the first 5 digits is odd, it can be made even by using 1, 3, 5, 7, or 9
for the 6th digit ... 5 choices.
-- If the sum of the first 5 digits is even, it remains even by using 2, 4, 6, 8, or 0
for the 6th digit ... 5 choices.
-- So, for any one of the 90,000 five-digit numbers, there are 5 choices for the 6th digit
that result in an even sum of all six.
-- So, there must be 450,000 suitable 6-digit numbers.
The largest 3 digit number whose digits are all primes is 777. The largest 3 digit number with different prime digits is 753.
The largest three digit prime number whose digits are all primes is 773.
1
279,999,720
992
The largest 3 digit number whose digits are all primes is 777. The largest 3 digit number with different prime digits is 753.
Find a four digit number whose digits will be reversed when multiplied by nine?
The largest three digit prime number whose digits are all primes is 773.
1
279,999,720
992
7777
940
111111
What is the units digit of the least whole number greater than 1000 whose digits are all different?
137?
91 since the ones digit is 8 less than 9 and the two digits, 9+1 = 10, a two-digit number.