The Holiday Puzzle:
"Alex and Brian are cousins. They are planning a four-day holiday in Venice and they each have 400 euros to spend. (They have already paid for their return flights and for their hotel room.) On the flight to Venice Alex and Brian discuss how they should each allocate their spending over the four days.
1. How many ways are there to cover a 2 x n rectangular grid with 2 x 1 tiles?
2. Imagine a ladder leaning against a vertical wall with its feet on the ground. The middle rung of the ladder has been painted a different colour on the side, so that we can see it when we look at the ladder from the side on. What shape does that middle rung trace out as the ladder falls to the floor?
1. Would you expect this compound to be more soluble in octanol or water? (The student will be shown the structure of an organic compound with functional groups that they will be familiar with from A-level/IB studies)
2. The relative solubility of a compound in octanol vs aqueous solution can be determined by putting a sample of the compound in a 1:1 mixture of octanol and aqueous solution and then measuring the concentration of the compound that has dissolved in each of the solvents. For one particular compound the relative solubility varies with pH as shown in the graph below. Can you interpret this graph?