Start with a box on its own
Each box holds one rule and always applies it. Your job is to name that rule.
Find an example that goes through one box on its own. Compare what went in with what came out, and write the rule down as an action: swap these two, move everything left, step this one on.
Above, A 3 C 5 goes into the circle box and C 3 A 5 comes out. The first symbol and the third have traded places. The other two are where they were. So the circle box swaps positions 1 and 3.
Check that action on a second example before you trust it.
1Find a box you can see on its own.
2Write its rule as an action.
3Follow the arrows in order.
Two boxes, one after the other
The square box has its own example. B 6 E 2 goes in and 2 E 6 B comes out. The whole string is back to front, so the square box reverses the order.
The question sends D 7 F 1 through the circle box and then the square box.
The circle box swaps positions 1 and 3, so D 7 F 1 becomes F 7 D 1. The square box reverses that, so F 7 D 1 becomes 1 D 7 F.
Do one box at a time and write the middle string down. Doing both at once is where the mistakes come from.
Use one box to uncover another
This is a new board. The boxes keep their shapes but hold new rules, so read them from scratch.
On this board, one box appears on its own. Find its rule first, then undo its action in the two-box example to uncover the other rule.
The triangle box has its own example: E 2 G 4 comes out as E 4 G 2, so it swaps positions 2 and 4.
The other example sends B 5 D 7 through the circle box and then the triangle box, and 7 B 5 D comes out. Swap positions 2 and 4 of 7 B 5 D to undo the triangle box, and you get 7 D 5 B. So the circle box turned B 5 D 7 into 7 D 5 B.
Try it
What does the circle box do?
- It reverses the order
- It swaps the first and third symbols
Show the answer
It reverses the order
B 5 D 7 read backwards is 7 D 5 B, which is what came out of the circle box.
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Practice Rule boxes