That ain't possible: the last digit of an odd number must always be an odd digit (1, 3, 5, 7, 9).
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There is no such number. If the four digits are even, the entire number is even, not odd.
There is no solution to this problem. If each digit can be used once only then we have 5 odd numbered digits (1,3,5,7,9) and 4 even numbered digits (2,4,6,8). To create the two numbers that are added together requires the following combinations of digits. 5 Odd & 1 Even ....when added these will generate 2 Even digits & 1 Odd digit but the remaining digits are 3 Even. 4 Odd & 2 Even. These will generate 3 Even digits OR 1 Even digit & 2 Odd digits but the remaining digits are 1 Odd & 2 Even. 3 Odd & 3 Even. These generate 3 Odd digits OR 2 Even & 1 Odd digits but the remaining digits are 2 Odd & 1 Even. 2 Odd & 4 Even. These generate 3 Even digits OR 2 Odd & 1 Even digits but the remaining digits are 3 Odd & no Even.
I cannot see how odd or even will determine the number of digits in the square root. For example:100 is an even number, and its square root is 10 (2 digits)121 is an odd number, and its square root is 11 (2 digits)Maybe the question is not phrased properly for what the questioner is asking.
The largest odd number that can be made with those digits is 9407 .
The one closest to the Middle if your sequence is of an even set of digits. The median will be a specific number if you have a sequence of odd digits.