The diagram below shows four cups in a row, labelled 1, 2, 3 and 4. Initially, there is a ball inside cup #3. In each move, the ball may be transferred to an adjacent cup. From cup #1, the ball can only go to cup #2, and from cup #4, the ball can only go to cup #3. After 2012 moves, which of the following statements about the ball is correct?

On a 4 x 4 chessboard shown in the diagram below on the left, we wish to place a minimum number of copies of the shape shown in the diagram below on the right, so that no more copies of this shape can be placed. Copies may be rotated. What is this minumum number of copies ?

The diagram below shows a cube with three of its faces labeled A, B and C and a 3 x 3 square with six of its squares labelled 1, 2, 3, 4, 5 and 6. The cube is tipped over so that face C lies on square 1, tippled over again so that face B lies on square 2, and so on until the cube lies on square 6. What is the sum of numbers of the squares on which the cube has laid with face B on top ?

The number of bicycles in the school bicycles lot is a three – digit number, and the number of bicycle wheels is also a three-digit number. These six digits are 2, 3, 4, 5, 6 and 7 in some order. At most how many bicycles are there ?

For any positive integers a and b, define a new operation a ….b which yield the remainder when the larger of a and b is divided by the smaller one. For example, 5….12 = 12…5 = 2. Given that ( 11…x )…11 = 2, what is the minimum value of x ?

In the expression 2…3…4…5, an operation sign ( addition, subtraction, multiplication or division ) is placed in each …. The same operation may be repeated. What is the largest two-digit number that can be obtained ?

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This chocolate cake is delicious.

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The weather is beautiful !

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He wrote the letter in two hours.

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They are producing motorbikes in Vietnam

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When did you start the project ?

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Their wedding will be held in a lovely church

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What is the weight of your suitcase ?

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How tall is Peter’s father ?

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The last time I met her was in 1999