Camping Challenge

Look carefully at the picture below and answer the questions.

1. How many tourists are staying at this camp?
2. When did they arrive: today or a few days ago?
3. How did they get here?
4. How far away is the closest village?
5. Where does the wind blow: from the north or from the south?
6. What time of day is it?
7. Where did Alex go?
8. Who was on duty yesterday? (Give their name)
9. What day is it today?

1. There are 4 people.
2. They arrived a few days ago, enough so that a spider web can appear on the tent.
3. Judging by the paddles, they got there with boats.
4. There is a hen walking around the camp, so the closest village is not far away.
5. The leaves of the trees are larger at the south side, so the wind must be blowing from the South.
6. The shadow is pointing towards West, so it must be morning.
7. Alex went to catch butterflies.
8. Since Peter is on duty today – cooking food for the group, it was Colin on duty yesterday.
9. Today is August 8. Watermelons ripen in August.

Perfect Day

This morning I woke up at 9 o’clock. My first job was to drink a glass of water and brush my teeth. After that, I ate an apple, 3 bananas (I love them!) and a toast with almond butter for breakfast. Then I went to the gym for one hour, took a shower there and came back home at eleven. Cooked a few pieces of chicken with some small potatoes for lunch, ate all of them. In the afternoon I started working on my projects while listening to classical music. In the evening I went for the 2nd time to the gym, did cardio for half-an-hour and after that visited my friend’s apartment. We had together one big pizza for dinner and in the end, I fell asleep on his couch.

As you can see, my entire day was perfect, except that my laptop keyboard broke. Can you figure out what’s wrong with it?

All of the numbers in the text are written using digit symbols except for the ones containing “one” (“one”, “eleven”, “first”). This inconsistency implies that the number “1” key on the keyboard is broken.

9 balls, 1 defective

You have 9 balls, 8 of which have the same weight. The remaining one is defective and heavier than the rest. You can use a balance scale to compare weights in order to find which is the defective ball. How many measurements do you need so that you will be surely able to do it? What if you have 2000 balls?

First, we put 3 balls on the left side and 3 balls on the right side of the balance scale. If the scale tips to one side, then the defective ball is there. If not, the defective ball is among the remaining 3 balls. Once left with 3 balls only, we put one on each side of the scale. If the scale tips to one side, the defective ball is there. If not, the defective ball is the last remaining one. Clearly we can not find the defective ball with just one measurement, so the answer is 2.

If you had 2000 balls, then you would need 7 measurements. In general, if you have N balls, you would need to make at least log₃(N) tests to find the defective ball. The strategy is the same: keep splitting the group of remaining balls into 3 (as) equal (as possible) subgroups, discarding 2 of these subgroups after a measurement. To see that you need no less than log₃(N) tries, notice that initially there are N possibilities for the defective ball and every measurement can yield 3 outcomes. If every time you get the worst outcome, you will make at least log₃(N) tries.

Drown or Burn

The ship you are traveling on crashes and you somehow succeed to reach the shores of an island. On this island however, a cruel tribe resides and decides to murder you. The tribals can not agree on how to do this, so they decide that if the first sentence you say is a lie, they will drown you, and if it is a truth, they will burn you. Luckily, you hear their conversation and come up with a plan. What do you tell them?

You can tell them “You will drown me”. This will result in a paradox – if your sentence is true, then they will drown you, but on the other hand will be forced to burn you, which is a contradiction. Similarly if your sentence if false. Therefore they will not have a choice except to give up on their plan.