Give a quick stream of consciousness before answering the following question. How many positive four-digit integers do not contain any digits other than 1 or 0 and are such that the sum of the first two digits equals the sum of the last two digits?\nOptions:\n(A) 3\n(B) 4\n(C) 8\n(D) 10\n(E) 12
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The sum of the first two (last two) digits cannot be 0 because 0000 is not a four-digit integer. If the sum of the first two digits is 1, two variants are possible: 1001 and 1010 (we have to remember that 0 cannot be the first digit). If the sum of the first two digits is 2, one variant is possible: 1111. In all, there are three numbers that satisfy the given conditions: 1001, 1010, and 1111.
The answer: (A).
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