Cubes And Cashier
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Volume of a Holey Cube Consider a solid wooden cube whose side has length L = 8 cm. If three holes of diameter D = 6 cm are drilled completely through, and perpendicular to, the centers of all the faces of the cube, what is the volume V of the remaining wood in the cube?
Divide & Conquer (hint) ABC is a general triangle and its area is equal to 132 cm square. The opposite side of edge A is divided in 4 equal parts and the opposite side of edge C in 3 equal parts. Straight lines join the point A to each quarter of line BC. Likewise, from point B to each third of line AB. How big is the area of quadrilateral DBEF? http://www.freepuzzles.com/puzzles/PuzzlePage.asp?PuzzleNumber=Geom025&CategoryID=1
Not Quite the Bull’s Eye The length of each side of the square ABCD is 10 cm. The shaded area EFGH is surrounded by 4 curves of quarter circle. How big is the shaded area EFGH?
Triplet Brothers There are 3 triplet brothers. They look identical. The oldest is John, he always tells the truth. The second is Jack, he always tells a lie. The third is Joe, he either tells the truth or a lie. Jimmie Dean went to visit them one day. He was wondering who was who. So he asked each person a question. He asked the one who was sitting on the left: “Who is the guy sitting in the middle?” The answer was “He is John.” He asked the one who was sitting in the middle: “What is your name?” The answer was “I am Joe.” He asked the one who was sitting on the right: “What is the guy sitting in the middle?” The answer was “He is Jack.” Jimmie Dean got really confused. Basically, he asked 3 same questions, but he got 3 different answers. Would you find out who is who for Jimmie?
Squares of 5 Consecutive Integers A^2 + B^2 + C^2 = D^2 + E^2 In the equation shown, A, B, C, D and E are 5 consecutive positive integers. What are they?
Cubes of 4 Consecutive Integers A^3 + B^3 + C^3 = D^3 In the equation shown, A, B, C and D are 4 consecutive positive integers. What are they?
Money Mix-Up Denny went into a back to cash a check. In handling the money, the cashier, by mistake, gave him dollars for cents and cents for dollars. He pocketed the money without examining it, and spent a nickel on his way home. He then found out that he possessed exactly twice the money of the check. He had no money in his pocket before going to the bank. What was the exact amount of the check?
Divide & Conquer (hint) ABC is a general triangle and its area is equal to 132 cm square. The opposite side of edge A is divided in 4 equal parts and the opposite side of edge C in 3 equal parts. Straight lines join the point A to each quarter of line BC. Likewise, from point B to each third of line AB. How big is the area of quadrilateral DBEF? http://www.freepuzzles.com/puzzles/PuzzlePage.asp?PuzzleNumber=Geom025&CategoryID=1
Not Quite the Bull’s Eye The length of each side of the square ABCD is 10 cm. The shaded area EFGH is surrounded by 4 curves of quarter circle. How big is the shaded area EFGH?
Triplet Brothers There are 3 triplet brothers. They look identical. The oldest is John, he always tells the truth. The second is Jack, he always tells a lie. The third is Joe, he either tells the truth or a lie. Jimmie Dean went to visit them one day. He was wondering who was who. So he asked each person a question. He asked the one who was sitting on the left: “Who is the guy sitting in the middle?” The answer was “He is John.” He asked the one who was sitting in the middle: “What is your name?” The answer was “I am Joe.” He asked the one who was sitting on the right: “What is the guy sitting in the middle?” The answer was “He is Jack.” Jimmie Dean got really confused. Basically, he asked 3 same questions, but he got 3 different answers. Would you find out who is who for Jimmie?
Squares of 5 Consecutive Integers A^2 + B^2 + C^2 = D^2 + E^2 In the equation shown, A, B, C, D and E are 5 consecutive positive integers. What are they?
Cubes of 4 Consecutive Integers A^3 + B^3 + C^3 = D^3 In the equation shown, A, B, C and D are 4 consecutive positive integers. What are they?
Money Mix-Up Denny went into a back to cash a check. In handling the money, the cashier, by mistake, gave him dollars for cents and cents for dollars. He pocketed the money without examining it, and spent a nickel on his way home. He then found out that he possessed exactly twice the money of the check. He had no money in his pocket before going to the bank. What was the exact amount of the check?
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