Answer: 103,845
This is a single number separated by a comma to make it more readable. This number is slightly over one hundred thousand.
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Step-by-step explanation:
The number is divisible by 5, so the units digit must be 0 or 5 based on the divisibility rule for 5. The units digit cannot be 0 because that would mean other digits would be larger, but only the hundreds digit is larger than the units digit. So the units digit must be 5.
The hundred thousands place must be the digit 1 since it is the only single digit value that is both a cube and a square.
The hundreds place can be a 1 or an 8 since they are cubes, but 1 is already taken so we are forced to pick 8 for the hundreds place. Note how the hundreds place (8) is larger than the units place (5)
The tens place can be 1, 4, or 9. But we can't pick 1 since its already taken. We also can't pick 9 since only the hundreds digit is larger than the units digit. So the tens place is stuck with 4
Solve this equation: (ones place)+(thousands place) = (hundreds place) to find that the thousands place must be 3. You should find that 5+x = 8 solves to x = 3.
Add up all the values found so far, then subtract the result from 21 to get the result 0. This means the final leftover place value (ten-thousands place) must be 0
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To recap:
Ones place = 5
Tens place = 4
Hundreds place = 8
Thousands place = 3
Ten-Thousands place = 0
Hundred-Thousands place = 1
So that's how I got the answer 103,845