ChatGPT: Sure, let's solve this number puzzle.

We want to find three digits A, B, and C such that the sum of the numbers AAA and BBB equals AAAC. We can start by noticing that since A and B are digits, the maximum value they can take is 9. Therefore, the maximum value of AAA and BBB is 999, and the maximum value of AAAC is 1998.

Let's start with the ones column, which is the easiest to solve. We know that A + B must equal C, so C can only be a digit between 0 and 9. Therefore, A + B = C or A + B = C - 10.

If A + B = C, then we can write:

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AAA
BBB
= AAAC
C

In this case, we have:

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A + B = C
A + B + A = C + 1 (since we carry over 1 from the ones column to the hundreds column)
A + B + B = A + 10C
Combining the first and third equations, we get:

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2A + 2B = A + 10C
Simplifying, we get:

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A = 5C - B
This equation tells us that A must be a multiple of 5, since B and C are digits and can only take values between 0 and 9. Therefore, we can try different values of A and C to see if we can find a value of B that satisfies the equations. Let's start with A = 5 and C = 1:

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555
BBB
= 556C

We know that B + 5 = C, so B = C - 5 = -4, which is not a valid digit. Therefore, we can try A = 10 and C = 2:

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1010
BBB
= 1022

We know that B + 1 = 2, so B = 1. Therefore, the solution is:

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A = 10
B = 1
C = 2
Let's check that this solution works:

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1010
191
= 1201

Therefore, the solution is A = 10, B = 1, and C = 2.

If A + B = C - 10, then we can write:

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AAA
BBB
= AAAC
C-10

In this case, we have:

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A + B + 1 = C
A + B + A = C + 1 (since we carry over 1 from the ones column to the hundreds column)
A + B + B = A + 10C - 10
Combining the first and third equations, we get:

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2A + 2B = A + 10C - 11
Simplifying, we get:

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A = 5C - 6 - B/2
This equation tells us that A must be an odd multiple of 5, since B and C are digits and can only take values between 0 and 9. Therefore, we can try different values of A and C to see if we can find a value of B that satisfies the equations. Let's start with A = 5 and C = 2:

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555
BBB
= 556C
C-10