Question 161
In a regular tetrahedron with vertices $A,B,C,D$, let $P,Q$ be the centers of the two faces sharing edge $AB$. What is the ratio of the volume of the original tetrahedron to the volume of tetrahedron $ABPQ$?
Problem:
Let $n$ be the smallest positive integer greater than $200$ that can be written as a sum of 5 consecutive integers, as a sum of 6 consecutive integers, and as a sum of 7 consecutive integers. What is $n$?
Problem:
Let $n$ be the smallest positive integer greater than $200$ that can be written as a sum of 5 consecutive integers, as a sum of 6 consecutive integers, and as a sum of 7 consecutive integers. What is $n$?