Alex lights a candle every ten minutes. Each candle burns for 40 minutes and then goes out. How many candles are alight 55 minutes after Alex lit the first candle?
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A rope is folded in half, then in half again, and then in half again. Finally the folded rope is cut through, forming several strands. The lengths of two of the strands are 4 m and 9 m. Which of the following could not have been the length of the whole rope?
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Mark plays a computer game on a 4 × 4 grid. Initially the 16 cells are all white; clicking one of the white cells changes it to either red or blue. Exactly two cells will become blue and they will always have a side in common. The aim is to make both blue cells appear in as few clicks as possible. With perfect play, what is the largest number of clicks Mark will ever need to make?
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A Kangaroo has a large collection of small cubes 1 × 1 × 1. Each cube is a single colour. Kangaroo wants to use 27 small cubes to make a 3 × 3 × 3 cube so that any two cubes with at least one common vertex are of different colours. At least how many colours have to be used?
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Toy kangaroos are packed for shipment. Each of them is packed in a box which is a cube. Exactly eight boxes are packed tightly in a bigger cubic cardboard box. How many kangaroo boxes are on the bottom floor of this big cube?
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A boy always speaks the truth on Thursday and Fridays, always tells lies on Tuesdays, and randomly tells the truth or lies on other days of the week. On seven consecutive days he was asked what his name was, and on the first six days he gave the following answers in order: Akbar, Ali, Akbar, Ali, Farooq, Ali. What did he answer on the seventh day?
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Rose plants were planted in a line on both sides of the path. The distance between each plant was 2 m. What is the maximum number of plants that were planted if the path is 20 m long?
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A house has 10 rooms. Ten boys stay in different rooms and count the number of doors in them. After that they sum all results and receive 25. What a proposition can't be true about number N of doors which led outside the house?
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Mike chose a three-digit number and a two-digit number. Find the sum of these numbers if their difference equals 989.
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