Pencils Puzzles

Puzzle 1 This is a puzzle but also a paradox. In this picture of my pencils you will see that I have seven red pencils and six yellow pencils.

Now let’s cut up the picture and rearrange the pieces — simply swapping the star piece with the moon piece. Just tap or click on the picture to see this happen. How about counting the pencils again? Now I make it six red pencils and seven yellow pencils. Can you work out how this happened?

Puzzle 2 Now we have a vanishing pencil. Again tap or click on the picture to see this happen.


Puzzle 1  The Changing pencils. This puzzle was devised in 1956 by Mel Stover, a Canadian magician and puzzler.

Mel Stover’s 1956 puzzle

If you study my pencils, you will notice that all the pencils change in length, either getting longer or shorter, but generally stay the same colour. Except that the fourth one along from the left changes from red to yellow. Quite how this works I don’t know.

Puzzle 2  The Disappearing Pencil. The principle is shown in the picture below. If you slide the top half of this drawing along one bar disappears and all the remaining bars increase in length. However If you add up the total length of the bars before and after (using the pink stripes), you will find they both add up to 42. To make the bar re-appear you simply slide back in the opposite direction.

how the puzzle works

The cleverness of the pencil puzzle above is that you don’t simply slide, you swap over, but the idea behind it is the same. The disappearing pencil only works if you don’t sharpen the pencils. Can you see why?

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