In the’Riddle of the boxes and ballsthe situation is this: there are three boxes, one containing only white balls, one containing only black balls, while the third is mixed, containing both colors (in the video attached to the article, the balls are blue and green, but it can be done with any color). Each box has a label indicating the color of the balls which contains the box, therefore: WHITE, BLACK, MIXED. Whoever put the labels, however, was completely wrong in assigning them and therefore they are all wrong.
By drawing a single ball However, from just one of the boxes it is possible to understand the contents of all three boxes and reorder the labels. Which box should the ball be drawn from?
To solve this riddle, you must first of all keep in mind the fundamental condition why ALL labels they are placed on the box wrong. Once this clarification has been made, we just need to reflect case by case, imagining what can happen if we fish the only ball available to us from each of the boxes:
- fishing from WHITE boxesif we draw a white ball we can be sure that the box in question is the box of MIXED balls (because it certainly cannot be the box of white balls, as it is written on the label), but if instead we draw a black ball, we could be in front of the BLACK as well as MIXED box;
- in the same way, fishing from BLACK boxif we draw a black ball we can be sure that the box in question is the box of MIXED balls (because it certainly cannot be the box of black balls, as it is written on the label), but if instead we draw a white ball, we could be in front of the WHITE as well as MIXED box;
- fishing from MIXED boxif we draw a white ball we can be sure that the box in question is the box of WHITE balls (because it certainly cannot be the box of white balls, as it is written on the label), and in the same way if we draw a black ball we can be sure that we are in front of the box of BLACK balls.
There solution is therefore to fish our only ball from the MIXED box:
- if the ball is whitewe can conclude that: the MIXED box must be labeled as WHITE and at this point – given that the box labeled as BLACK is wrong – we pass its label onto the box that initially read WHITE and label the box initially labeled as BLACK as MIXED;
- if the ball is blackwe can conclude that: the MIXED box must be labeled as BLACK and at this point – given that the box labeled as WHITE is wrong – we pass its label onto the box that initially read BLACK and label the box initially labeled as WHITE as MIXED.
