## Starry banner brainteaser

By David Shaw, 18 August 2021

**Difficulty: Tricky**

Kirk is designing a banner for an astronomy club. They want to put some stars on the banner, in straight lines. Here are Kirk’s rules:

- The banner needs to have 5 straight lines, with 4 stars in each line.
- None of the straight lines can have 5 stars in them.
- The straight lines can go up and down, or left and right, or at a diagonal at any angle.
- Stars can be in multiple straight lines at the same time.

The stars that Kirk wants to use are expensive, so they want to use as few as possible. What’s the best design you can make?

13 stars: good

11 stars: great

10 stars: excellent!

**Scroll down or click for a hint, or the answer!**

## Brainteaser hint

This puzzle is easier if you start by drawing the lines. If you put a star where 2 lines meet, the star will be in both lines!

## Brainteaser answer

There are many answers, so there are lots of ways to approach this puzzle. One simple way is to start with the idea of a grid. With 2 lines across and 2 lines down you’ll have 4 lines of 4 stars, using 12 stars. You can find a sneaky diagonal line by adding just one more star.

What if you use the same star in 3 different lines? It will take 9 more stars to finish those lines. If you create 2 more lines that cross those 3, you’ll have 5 lines using 11 stars total.

To make 5 lines only using 10 stars, every single star needs to be in 2 lines. This is quite tricky to design, but you can do it with a star pattern.

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18 August, 2021 at 2:57 pm

In the first answer you gave, you can actually do it with one less star by shifting the diagonal line to the right by one star.

The diagonal line can start from the 4th star on the top, go through the 3rd star on the second row, then continue through to the 3rd star on the second column, and finally on the bottom star of the 1st column.

18 August, 2021 at 3:00 pm

true! there’s one already there that I completely missed!