THE’Owl riddle It is a very simple puzzle, but which confuses us because of an automatism of our mind. The situation is this: there is a farmer who shows up in a new market and wants to sell his egg. Every day, he succeeds in sell punctually half of those he has, more half an egg. If After three days he exhausted all the eggs he had available, how many eggs did he have at the beginning? Let’s see the solution.
The solution to the egg investigation
On two feet, the solution does not seem to exist: “How is it possible that he can sell half an egg? He can’t break them!”. And it is precisely here that the “deception” is: we are led to think that since the farmer sells every day half of the eggs it has, then the initial number will surely be even So that you can actually divide it in half. Except that now we are half egg to sell, but the eggs cannot be divided divided! And in fact here is the “trick”: if Let’s start with an odd number Of eggs, dividing in the middle we will have a number “half” – for example if they were 9, we would have 4.5 eggs – and so, adding the half egg that we add, we get an integer – in our example, we go from 4.5 to 5.
At this point, to find the solution we can do some attempt (or set up an equation, but in this case the equation is much more complex than the solution, which is extremely intuitive!). Let’s start with the intuition: since the days available are only 3, the odd number from which the eggs started cannot be too high and therefore we can afford to go for attempts, Starting from the smallest odd number after 1, that is 3:
- If the initial eggs were 3after a day we would have sold half more half an egg, then 1.5 + 0.5 = 2 eggs sold, thus remaining with 3 – 2 = 1, only one egg. On the second day, we would have sold half of our remaining egg again more half a half egg – therefore 0.5 + 0.5 = 1 – but we had only one egg available! We remained without eggs in just two days. So 3 cannot be our solution;
- We therefore increase the value of the odd number Starting from 5 Initial eggs: on the first day we would have sold 2.5 + 0.2 = 3, thus remaining with 5 – 3 = 2 eggs in hand. We have reached an equal number of eggsand as we said at the beginning this makes it impossible to find a solution! It is therefore not 5 our number, let’s go on with the reasoning;
- Let’s start with 7 eggs: The first day we would sell half more half an egg, then 3.5 + 0.5 = 4, thus remaining with 7 – 4 = 3 eggs. At this point, with 3 eggs, we already know what will happen, we saw it in case 1: after 2 days, the eggs will be exhausted, because we will go from three eggs to have 1 to the second day, and from 1 egg to Have 0 the third.
Our solution is therefore 7 eggs!
