There is a 3-digit ABC. If you add up 5 3-digit ACB, BAC, BCA, cab and CBA, they are equal to 3194.
What is the three digit ABC equal to?
How high is your digital ability?
ABC answer
Solution 1:
3194 + ABC = 222(A + B + C)
14 X 222 + 86 + ABC = 222(A + B + C)
86 + ABC = k222
when k = 2
ABC = 358
Solution 2:
ABC = 358
Add the five hundreds to get a + 2B + 2C
From 3194, the ten digit is 9, so the carry from 10 to 100 is not 4, of course, it can not be 1 or 0. In that case, if the number is too small, there will be no solution. So we get:
A + 2B + 2C = 28 (1) or
A + 2B + 2C = 29 (2)
The addition of 5 bits can only be 2 or 3
2A + 2B + C = 24 (3) or
2A + 2B + C = 34 (4)
It can be seen from the above that the C-bit is even
If (4) holds, use (4) - (1) = 5 respectively
A - C = 5 or
(4)-(2)= 6
A - C = 6
C = 2, a = 7 or a = 8
C = 4 A = 9
Neither of them is correct. Therefore (4) does not hold.
Then the sum of five tens 2A + B + 2C = 27 (5)
Or 2A + B + 2C = 37 (6)
If it is 37, then (6) - (3) = C - B = 13 is not true!
Get (1), (3) (5) or (2), (3), (5) solution, calculation is OK!