Problem list
- How many turns does the small circle make? A rolling circle's turn count comes from the path of its centre, not the length it touched
- How many cubes have 2 painted faces? For N×N×N: 3 faces is always 8, 2 faces is 12×(N−2), 1 face is 6×(N−2)², 0 faces is (N−2)³
- Into how many pieces do 4 lines cut the paper? Do not try to count the regions
- In how many ways can the three chosen rods form a triangle? Whether three lengths make a triangle rests on one test: the longest must be less than the other two added
- How many triangles are there in the figure? To count shapes, do not chase them with your eyes — find out what has to be chosen to pin one down
- How many squares are there altogether? Do not count in the order you spot things — count in the order they are determined
- How many squares does the diagonal pass through? Counting crossings is the quick way
- How many matches are needed? "The first one is special; after that the growth is steady
- What do the three "?" faces add up to? Hunting for which faces are opposite means fresh work for every net
- How many diagonals can be drawn in total? Count from one corner, multiply by the number of corners, then halve
- How many lines of symmetry does it have? Many people count only the corner-to-corner lines and stop at half the answer
Area Problems Angle Problems Length Problems Volume Problems Hard Problems Standard Problems