Question 1
**Printed examination instructions.** Answer the following 5 questions. Write down your answer in the space provided after each question. Each question is worth 8 points. Time limit: 60 minutes.
The diagram shows a network of water pipes, with eight taps, each shown by a symbol ×, at positions A, B, C, D, E, F, G and H. Water enters along three pipes at the left, indicated by →, and cannot pass a tap that is “off”. Each tap is either “on” or “off”. How many choices of taps in the “on” position result in water coming out of the pipe at the extreme right, assuming no more than three taps can be “on” at the same time?
The diagram shows a network of water pipes, with eight taps, each shown by a symbol ×, at positions A, B, C, D, E, F, G and H. Water enters along three pipes at the left, indicated by →, and cannot pass a tap that is “off”. Each tap is either “on” or “off”. How many choices of taps in the “on” position result in water coming out of the pipe at the extreme right, assuming no more than three taps can be “on” at the same time?