Question 89
a) Severina wrote a positive integer on each side of a square. She then wrote at each vertex the product of the numbers on the two sides meeting there. The numbers on one pair of opposite sides sum to 60, and those on the other pair sum to 85. What is the sum of the numbers written at the vertices?
b) Catarina wrote a positive integer on each face of a cube. She then wrote at each vertex the product of the numbers on the three faces meeting there. If the vertex numbers sum to 105, what is the sum of the face numbers?
b) Catarina wrote a positive integer on each face of a cube. She then wrote at each vertex the product of the numbers on the three faces meeting there. If the vertex numbers sum to 105, what is the sum of the face numbers?