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How good are you at numbers?

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!