Let’s consider a grid like the one shown in the image, with 6 almonds on each of the four sides and 4 almonds in the center. By moving the almonds one by one from the center to the sides and making some exchanges, the count of almonds per side remains equal to 6. But how is it possible that by adding 4 almonds the result does not change?
We see it in this article.
The paradox of the disappearing almonds
On a square-shaped sheet, a grid is drawn so that the sheet is divided into parts: 4 on each side and one in the center. On the grill come almonds as follows:
Counting the almonds, we can see that we find 6 on each side, while 4 in the center.
At this point we take an almond from the center and move it to one of the four sides, and then we move one of the almonds present on the corner inside one of the sides adjacent to the corner, obtaining the following configuration:
If we repeat the count of almonds, we can notice that we continue to have 6 on each side, while in the center we now only find 3. But how is this possible? Where did the fourth almond that was present in the center go, if the count of almonds on each side did not change?
We continue the process by gradually moving the almonds from the center towards the edge, repeating the operation described above.
When we arrive at having the center free of almonds, we realize that the number of almonds on each side has not changed, however, they are still 6.
And here we arrive at the paradox: same number of almonds on each side compared to the initial configuration, but no almonds in the center. Where did the 4 missing almonds disappear to?
The solution to the paradox
The solution may not be immediate at first glance, but it is simpler than you think.
The “trick” is to have moved from time to time an almond from the corner of the grid to one of the internal quadrants on each side.
In fact, taking the initial configuration again, we can note that in the beginning the only boxes containing two almonds were those on the 4 corners of the grid: this means that the two almonds present in the corner were counted on two different sides, that is, both almonds they made a double contribution.
In the following steps, we moved an almond from the center to the side, bringing the number of almonds present on that specific side to 7, but we also moved one of the almonds present in the corner towards the adjacent side. This brought the number of almonds on the affected side back to 6, and equally 6 almonds remained on the adjacent side, having simply moved one of its almonds from one square up.
To avoid doubts, watch the attached video!