Triangular matrix

If U1, U2 are upper triangular and L1, L2 are lower triangular, which of the following are triangular?  U1 + U2  U1U2  U12  U1 + L1  U1L1  L1 +...
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The sunrise problem

Two women start walking at the sunrise, one from point A to B and another from point B to A. The pass each other exactly at noon. The first...
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