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The largest three-digit number with a digit sum of 10 is 910. This can be determined by maximizing the hundreds place first, setting it to 9, and then adjusting the tens and units places to reach a total digit sum of 10. In this case, using 1 for the tens place and 0 for the units place achieves the desired sum.
105 is the sum
24
Add the last digit (units digit) to twice the previous digit (tens digit). If this sum is divisible by 4, so is the original number.
Seven of them.