John is out with his class of 25 boys to a local park. Each guy has a remote controlled car with them. The park has a racetrack that allows 5 cars to be raced at once. Their teacher, Mr. Ted, declares that the top three fastest cars get ice cream.
How many races are required to determine the 3 fastest cars?
Four friends need to cross a dangerous bridge at night. Unfortunately, they have only one torch and the bridge is too dangerous to cross without one. The bridge is only strong enough to support two people at a time. Not all people take the same time to cross the bridge. Times for each person: 1 min, 2 mins, 7 mins and 10 mins. What is the shortest time needed for all four of them to cross the bridge?
The initial solution most people will think of is to use the fastest person as an usher to guide everyone across. How long would that take? 10 + 1 + 7 + 1 + 2 = 21 mins. Is that it? No. That would make this question too simple even as a warm up question.
Let’s brainstorm a little further. To reduce the amount of time, we should find a way for 10 and 7 to go together. If they cross together, then we need one of them to come back to get the others. That would not be ideal. How do we get around that? Maybe we can have 1 waiting on the other side to bring the torch back. Ahaa, we are getting closer. The fastest way to get 1 across and be back is to use 2 to usher 1 across. So let’s put all this together.
1 and 2 go cross
2 comes back
7 and 10 go across
1 comes back
1 and 2 go across (done)
Your friends are coming over to your birthday party. Your mum has bought this delicious giant doughnut for you guys. Unfortunately she had to go somewhere. Now you have to serve all of them including you.
There are a total of nine kids including you. None of you would mind a smaller piece. Can you cut this doughnut into nine pieces in just three straight cuts?
You can see the figure or draw one of your own. The scenario is as shown. There are three houses represented with the triangle over the square. There are three utilities: W, G and E representing water, gas and electricity respectively.
Can you draw a line and get each utility into every house (9) total lines without ever crossing any line?