I am five digit number greater than 40,000 but less than 70,000.My ones digit is more than my ten thousands digit.All my other digit are the same.The sum of my gigit is 19.What number am i?

The fifth digit can only be 4,5, or 6

let's start with the largest case
6X,XX7 , where X is the same
6 + 3x + 7 = 19
3x = 6
X = 2
one case: 62227

if the unit digit is k, it should be clear that
19-(6+k) must be a multiple of 3
and that is true only of x = 2

how about starting with 5
5XXX6 or 5XXX6 etc
again: 19 - (5+K) or 14-k has to be a multiple of 3 and k>5
how about k = 8, which would give us
5XXX8, and 5+3x+8 = 19 ----> X = 1
second case: 51118

last possible case:
4XXX5, or 4XXX6, or 4XXX7 etc
19-(4+k) or 15-k has to be a multiple of 3, and k > 4
k = 9 would work
then 4+ 3X + 9 = 19 -----> X = 2
third case: 42229

Three numbers work:

62227
51118
42229

Let's break down the information given step by step:

1. The number is greater than 40,000 and less than 70,000.
2. The ones digit is more than the ten thousands digit.
3. All the other digits are the same.
4. The sum of the digits is 19.

From the given information, we can conclude:

1. Since the ones digit is more than the ten thousands digit, the possible values for the ten thousands digit are 1, 2, 3, 4, 5.
2. All the other digits are the same, so the possible values for the other four digits are 1, 2, 3, 4, 5, 6, 7, 8, 9.
3. The sum of these four digits is 19, so we need to find four digits that have a sum of 19.

Trying different combinations of digits, we find that the only combination that satisfies all the conditions is:

Ten thousands digit: 4
Other four digits: 6, 6, 3, 4

Therefore, the number is 46,634.

To solve this problem, we can break it down into steps:

1. Start with the given information: We have a five-digit number, greater than 40,000 but less than 70,000.
2. Identify the criteria: The number's ones digit is more than its ten thousands digit, and all the other digits are the same. The sum of all the digits is 19.
3. Determine the range of possibilities: Since the number is greater than 40,000 and less than 70,000, we know that the ten thousands digit can only be 4, 5, or 6.
4. Calculate the sum of the digits: Since all the digits are the same (except for the ones digit), we can calculate the sum of the digits in terms of the repeating digit. Let's call the repeating digit "x":

ten thousands digit + thousands digit + hundreds digit + tens digit + ones digit = 19
(4, 4, 4, 4, x) or (5, 5, 5, 5, x) or (6, 6, 6, 6, x)

5. Solve for "x": Substitute the repeating digit into the equation to find the value of "x".

For (4, 4, 4, 4, x):
4 + 4 + 4 + 4 + x = 19
16 + x = 19
x = 3

So, one possibility is 44,433.

For (5, 5, 5, 5, x):
5 + 5 + 5 + 5 + x = 19
20 + x = 19 (not possible, as the sum cannot be greater than 19)

For (6, 6, 6, 6, x):
6 + 6 + 6 + 6 + x = 19
24 + x = 19 (not possible, as the sum cannot be greater than 19)

6. Determine the final answer: Since the sum of the digits is 19, and the ones digit is more than the ten thousands digit, the number must be 44,433.