1. Cut a square piece of paper with the side length of 1 foot into five rectangles with the perimeter of 2 feet each. They are not necessarily congruent (of the same size and shape). How many of them are squares?
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2. Jane set out on foot from home to her granny. At 12.00, when she was L kilometers away from home, a cyclist caught up with her, picked her up and dropped her off L kilometers away from the destination point. After that, she arrived at her granny's cottage at 14.00. How long will it take Jane to walk back, given that she was transported by bicycle at twice her normal walking speed?
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3. Three frogs in the swamp jumped in turn. Each landed exactly in the middle of the segment between the other two. The jump length of the second frog is 60 centimeters. Find the jump length of the third frog.
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4. The green triangles are placed on the 8x8 board. Each triangle covers exactly half of the square and does not cover the other squares. The triangles do not touch each other. What is the maximum possible number of triangles on the board?
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5. There are 10 kids in a line. In total, girls and boys had equal numbers of nuts. Each kid gave a nut to each of those standing to their right. Now the girls have 50 more nuts in total than boys. How many girls are there in the line?
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6. A dog and a cat simultaneously grab a big sausage with their teeth from different sides. If the dog bites off his piece and runs away, the cat gets 300 grams more than the dog. If the cat bites off his piece and runs away, the dog will get 500 grams more than the cat. How much sausage will be left if they both simultaneously bite their pieces and run away?
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7. The first line shows that the product of three decimal fractions is another decimal fraction.
1.2 × 3.4 × 5.6 = 22.848
Replace the six asterisks in the second line by non-zero digits
*.* × *.* × *.* = 10
so that the product of the three decimal fractions is equal to 10. Some of the digits can be the same. What is the sum of the six digits?
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8. Draw a closed polyline that intersects each of its line segments exactly once at right angles (90°). What is the least possible number of sides that polyline can have?
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9. There are 1, 2, 3, 4, 5 and 6 nuts in six boxes. In one step you can move from one box to another exactly as many nuts as there are already in the other box. In other words, if a box contains 3 nuts, you can only add three more nuts. What is the largest number of nuts that can be collected in one box by such steps?
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10. Find a six-digit number whose first digit is 6 times lower than the sum of all the digits to its right, and whose second digit is 6 times lower than the sum of all the digits to its right. What is the second digit of the number?