Archived Stumpers (with solutions)
STUMPER #1.7: NUMBER PLAY
(Did you solve something differently? There's almost always more than one way to solve
a math problem. Sometimes there's even more than one correct solution!)
Return to this week's stumpers View all archives Return to Math Gym home
1. Triangular and Square
___A square number is a number you can represent with x's in the shape of a square. A triangular number is a number you can represent with x's in the shape of a triangle. In the picture below, you can see that 9 (on the left) is one example of a square number, and 6 (on the right) is one example of a triangular number:
xxx x x
xxx x x x
After the number 1, what's the first number that's both triangular and square?
36 (a square with 6 rows and a triangle with 8 rows).
2. Different Halves
___A teacher offered a prize to the student who could figure out what half of 8 was. One student said 0, one said 3, and one said 4. The teacher realized that each student actually deserved a prize. Why?
Half of 8 is 4, but the TOP half of 8 is 0, and the RIGHT half of 8 is 3.
3. What Comes Next ?
1 2 1 1
1 1 1 2 2 1
3 1 2 2 1 1
1 3 1 1 2 2 2 1
1113213211. Each row describes the row above it; for example, the second row says that the first row has "one 1"; the third row says the second row has "two 1s"; the fourth row says the second row has "one 2, one 1;" the fifth row says the fourth has "one 1; one 2; two 1s," and so on.