Question 27. A 3x4x5 cuboid consists of 60 identical small cubes. A termite eats its way along the diagonal from P to Q. This diagonal does not intersect the edges of any small cube inside the cuboid. How many of the small cubes does it pass through on its journey? If you take a closer look at the cuboid, what is important to note is that the question states that the diagonal does not intersect the edges of any small cube. That means that the termite is crossing along the faces of the small cubes. This we can easily count how far it crosses. On the front face, to cross from left to right, the termite has to go through 4 different faces. So we get 4. Then, going up, it has to cross through 3 faces. So we add 3. And finally, it has to cross 2 faces to go to P inwards. So we do plus 2. And we can't forget the first cube that it started, which wasn't accounted for in this method. So we add 1. When we do 1 plus 4 plus 3 plus 2, we get our answer, which is C, 10.

cuboid

diagonal

small cubes

termite path

intersection