Between the Screws - A Logic Puzzle

Introduction

I originally wrote this puzzle for the magazine of a local Role-Playing Games’ club, back in high school. It was originally written in Hebrew, but is presented here in its English translation.

The Puzzle Itself

When Nom the gnome went to build his new airplane “Little Wing”, he ran into a funny situation when he wanted to attach the wing to the body of the plane.

To do that, he had to use four screws in a particular order, using four screwdrivers of four different colours - one of them green. Furthermore, each screw had a different shape and a different length.

Your mission is to find out the order in which the screws were attached, their lengths, shapes, and the colour of the screwdriver used for each screw.

1. The screw that the gnome used the last was longer than the screw that needed the blue screwdriver, but was less than twice its length. (Albeit there is a screw that is twice as long than the one needing the blue screwdriver.)
2. The diamond-shaped screw was screwed after the screw with the blue screwdriver, but before the 6cm-long screw.
3. Only once was a shorter screw used right after a longer one.
4. The screw needing the red screwdriver, which isn’t the hexagonal one, was the last. The diamond-shaped screw did not come immediately before it.
5. The triangular screw came before the 2cm-long screw.
6. The screw needing the purple screwdriver is 8 cm long, did not follow the 2cm long screw.
7. The 4cm long screw was not the square-shaped one.

The solution can be found below.

Solution

From the puzzle the following data can be directly gathered:

• Screw lengths: 2cm, 4cm, 6cm and 8cm.
• Screwdriver colours: green, blue, red and purple.
• Screw shapes: square, diamond, hexagonal, and triangular.

Based on hint #1, we can tell that the scren needing the blue screwdriver and the final screw were either 4cm and 6cm long respectivly or 6cm and 8cm respectively, as no other allocations fullfill the hint. According to hint #2 we know that the 6cm long screw was either 3rd or 4th. If the 6cm screw was 4rd then, then the 4th screw must be 8cm (in accordance to hint #1). However, then the 3rd screw must be the one needing the blue screwdriver which is impossible according to hint #2, which means it must be at 1st or 2nd. Therefore, the 6cm screw was the 4th screw and the blue screwdriver was used for the 4cm screw. So far we have:

• 1st or 2nd - 4cm - Blue
• 2nd or 3rd - Diamond
• 4th - 6cm

All mutually exclusive.

According to hint #4 we know that the 4th screw needed the red screw driver and that it wasn’t the hexagonal one. Therefore, we know that «4th - 6cm - red - Not Hex». Hint #4 also tells us that the diamond shaped screw did not come immediately before it. Thus the diamond shaped screw must have been the 2nd one, and the 4cm screw must have been the 1st. So what we have so far is this:

• 1st - 4cm - Blue
• 2nd - Diamond
• 4th - 6cm - Red - Not Hexagonal

Now according to hint #3 we know that the order cannot be 4cm→2cm→8cm→6cm because that would mean two shorter screws have followed two longer ones. So we have:

• 1st - 4cm - Blue
• 2nd - 8cm - Diamond
• 3rd - 2cm
• 4th - 6cm - Red - Not Hexagonal

According to hint #5 the triangular screw preceded the 2cm screw, so it must have been the 1st screw. Since the 4th screw is not hexagonal screw, the hexagonal one must therfore be the 3rd screw, and the 4th screw must be the square screw. Thus, we have:

• 1st - 4cm - Blue - Triangle
• 2nd - 8cm - Diamond
• 3rd - 2cm - Hexagonal
• 4th - 6cm - Red - Square

Now all we have left to determine are the colours of the 2nd and 3rd screwdrivers. According to hint #6 we know that the 8cm screw was used with the purple screwdriver, so the 2nd screwdriver must have been purple and the 3rd screwdriver was green.

Our final results are: