2 out of 3
When Jim rolled some dice, the scores had the same product and sum. How many dice did Jim roll?
2 out of 3
What is the smallest number of additional squares that must be shaded so that this figure has at least one line of symmetry and rotational symmetry of order 2?
2 out of 3
A cube is rolled on a plane, landing on the squares in the order shown. Which two positions had the same face of the cube touching the surface?
3 out of 3
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
3 out of 3
What are the possible dimensions of a rectangular hallway if the number of tiles around the perimeter is exactly half the total number of tiles?
3 out of 3
ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?
3 out of 3
Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?
3 out of 3
The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain what happens when this shape rolls along with a plank of wood on top of it.
3 out of 3
Can you mentally fit the 7 SOMA pieces together to make a cube? Can you do it in more than one way?
3 out of 3
Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of the pictures.
