How many matches are needed?
A normal-level "Count" problem."The first one is special; after that the growth is steady." Almost every counting-pattern problem can be put into this shape.
GivenSquares are joined in a row, one match per side, until there are 10 of them.
Hints
- The first square takes 4 matches. Nothing surprising yet.
- Now the second square. Its left side is already there from the first square, so only 3 new matches are needed.
- The third, the fourth and every one after take 3 each. Once the pattern is steady, it is just arithmetic.
- For 10 squares: 4 for the first, then 3 for each of the other 9. 4 + 3 × 9 = 31.
- Check it another way. There are 11 vertical matches (one more than the number of squares) and 10 horizontal ones along the top and again along the bottom: 11 + 10 + 10 = 31. Same answer.
Answer 31
More "Count" problems
- How many turns does the small circle make?
- How many cubes have 2 painted faces?
- Into how many pieces do 4 lines cut the paper?
- In how many ways can the three chosen rods form a triangle?
- How many triangles are there in the figure?
- How many squares are there altogether?