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100 hundred-digit numbers in 100x100 - All-Russian MO 2004 Regional (R4) 9.5

Source:

September 27, 2024
combinatoricsnumber theorydivisible

Problem Statement

The cells of a 100×100100 \times 100 table contain non-zero numbers. It turned out that all 100100 hundred-digit numbers written horizontally are divisible by 11. Could it be that exactly 9999 hundred-digit numbers written vertically are also divisible by 1111?
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