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A number consists of 3 digits whose sum is 10. The middle digit is equal to the difference of the other two and the number will be increased by 99 if its digits are reversed. What is the square of the number?
172225
xyz- is the number and we have: x+y+z=10 ---->(1) y=z-x ---->(2) 100x+10y+z+99=100z+10y+x ---->(3) xyz^2=?
(3) => 99z-99x=99 => z-x=1 => z=x+1 (2) => y=z-x=x+1-x=1 (1) => x+y+z=x+1+(x+1)=10 => x=4 => z=5 xyz=415 xyz^2=415^2=172225
514 is the number
5+1+4 = 10 5-1 =4 514 - 415 = 99
I'm thinking of a number.
What is the number?
The year 1978 is such that the sum of the first two digits and the latter two digits is equal to the middle two digits, i.e. 19 + 78 = 97. What is the next year (after 1978) for which this is true?
A five-digit number is formed using digits 1,3,5,8 and 9 without repeating any one of them. What is the sum of all such possible numbers?
