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What is the sum of the digits of the largest 4-digit palindromic number which is divisible by 15?

Weekly Problem 23 - 2015
Can you simplify this algebraic expression with many divisions?

The diagram shows the net of a cube. Which edge meets the edge X when the net is folded to form the cube?

How many routes are there in this diagram from S to T?

The information display on a train shows letters by illuminating dots in a rectangular array. What fraction of the dots in this array is illuminated?

Weekly Problem 45 - 2008
The diagram shows a regular pentagon with two of its diagonals. If all the diagonals are drawn in, into how many areas will the pentagon be divided?

How many zeros are there at the end of $3^4 \times 4^5 \times 5^6$?

Which of these five algebraic expressions is largest, given $x$ is between 0 and 1?