A three digit number with a ten digit number of 0 is exactly 67 times the sum of the three digit numbers. After exchanging one digit with a hundred digit number, another three digit number is obtained. If the new three digit number is m times the sum of the three digit numbers, then M=______ ．

A three digit number with a ten digit number of 0 is exactly 67 times the sum of the three digit numbers. After exchanging one digit with a hundred digit number, another three digit number is obtained. If the new three digit number is m times the sum of the three digit numbers, then M=______ ．

Let the single digit be a and the hundred digit be B. according to the known conditions, there are 100A + B = 67 (a + b) and 100b + a = m (a + b). By adding the two formulas, we can get 100 (a + b) + (a + b) = (67 + m) (a + b). By dividing both sides by (a + b), we can get 67 + M = 101, then M = 34

Verification: a three digit hundred digit number and a single digit number exchange position, then the number and the original can be divided by 99
It is helpful for the responder to give an accurate answer

Let the original three digits be XYZ
(100x+10y+z)-(100z+10y+x)
=99(x-z)
So it must be divisible by 99

If the sum of the single digit and the ten digit of a two digit number is greater than 10, the sum of the two digits plus 36 is exactly equal to the two digits obtained by swapping the two digits
Find the original two digits, write the reason, column inequality

Let X be one digit and y be ten digits
X + Y > 10 and X, Y > 0
10Y+X+36=10X+Y
X-Y=4 X+Y>10
So x = 8 or 9
Y = 4 or 5
So the original two digits are 48 or 59