In the word KANGAROO Bill and Bob replace the letters by digits, so that the resulting numbers are multiples of 11. They each replace different letters by different digits and the same letters by the same digits. Bill obtains the largest possible such number and Bob the smallest. In both cases one of the letters is replaced by the same digit. Which digit is this?
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The modern statue on the diagram was made by cutting a rectangular prism out of a stone that originally had the shape of a cube. The volume of the original cube was 512dm to the power of 3. What is the surface area of the statue on the diagram?  More...

Alan was calculating the volume of a sphere, but in the calculation he mistakenly used the value of the diameter instead of the radius of the sphere. What should he do with his result to get the correct answer?  More...

Given a square ABCD with side 1, all squares are drawn that share at least two vertices with ABCD. What is the area of the region obtained by stretching a rubber band around the squares?  More...

In a list of five numbers, the first number is 2 and the last number is 12. The product of the first three numbers is 30, the product of the three in the middle is 90 and the product of the last three numbers is 360. Which number is in the centre of the list?  More...

Two identical cylinders are cut open along the dotted lines and glued together to form one bigger cylinder – see the figure. What can you say about the volume of the big cylinder compared to the volume of one small cylinder  More...

Two identical cylinders are cut open along the dotted lines and glued together to form one bigger cylinder – see the figure. What can you say about the volume of the big cylinder compared to the volume of one small cylinder  More...

Which of the following is the complete list of the number of acute angles a convex quadrilateral can have?  More...