Eleven students each suggest one color. The twelfth student says “try firing the Spectral Blaster.”

Does this pattern work? No. Why? Because it violates… RULE 1: All colors present must appear equally often. (equality rule)

Note: This pattern violates ALL the rules, but you only say one rule at a time.

Twelve students each suggest one color. The thirteenth student says “try firing the Spectral Blaster.”

Does this pattern work? It satisfies RULE 1 (equality rule), but No – it still fails. Why? Because it violates… RULE 2: All color patterns must be different (different pattern rule.)

One child wishes to try something similar and then tries firing the Spectral Blaster, but it still does not work. The blue pattern is different from the other two, but they are the same so it still fails because of RULE 2: All color patterns must be different (different pattern rule.)

The next group suggests the following pattern which does not violate Rule 1 (equality rule) or RULE 2 (different pattern rule,) but it does violate RULE 3 (all patterns must have mirror symmetry.)

Blue and purple do have mirror symmetry, but not red.

The next student group suggests the following pattern which satisfies RULE 2 (different pattern rule) and RULE 3 (all patterns must have mirror symmetry) as you can see on the next slides…

Red has mirror symmetry.

Blue has mirror symmetry.

Blue has mirror symmetry.

Unfortunately it fails RULE 1 (equality rule.)

The next group suggests this little pattern. Does this work?

RULE 1 is certainly satisfied (equality rule.)

Red has mirror symmetry.

Blue has mirror symmetry.

Purple has mirror symmetry.

Unfortunately the patterns for all colors are all the same… two squares separated by two squares.

This violates RULE 2 (different pattern rule.)

The next group of students suggest another little pattern. Does it satisfy RULES 1, 2 and 3?

Red is symmetric.

Blue is symmetric – and the two blue squares are separated by only two spaces. Red was separated by three. This means the red and blue patterns are different.

Purple is symmetric – and the two purple squares are separated by only one space.

RULE 1, 2 and 3 are satisfied. Unfortunately RULE 4 is not.

What do you think RULE 4 is? Many wrong, but interesting answers should flow. Cap the discussion after a minute or two.

RULE 4: The lines of mirror symmetry must all be different (different axes.)

Unfortunately in spectral blast above – the red and purple lines of mirror symmetry are the same. The good thing is – that’s all the rules! Can you find a pattern that satisfies everything.

Does this work? Are all four rules satisfied?

PS. We could make another rule: there need to be at least two colors, but I’ll leave it up to your students if they ever discover the trivial solution of a single colour pattern.

Red has mirror symmetry.

Blue has mirror symmetry.

Purple has mirror symmetry.

This is our first successful shot from our spectral blaster.

Find a solution using twenty spaces and five colors.

Here is one solution.

Experiment!

Being hit by a spectral blast doesn’t kill, but it is disorienting. Here is a sample of what a temporarily blinded individual sees. For another, related puzzle on Spectral Blaster Rings look here.