# Let's do triangles!

1 post

 I don't know if this is any more appealing in terms of gameplay, but the idea is just to cut each rectangle in two along a diagonal, doubling the number of pieces. I have two slightly different rulesets for this: **Type A:** When swapping two triangles, try each of the following in turn. 1. do a scaling and translation on each triangle as normal to send each outline to the other 2. do a horizontal or vertical reflection on each triangle, then continue with step 1 3. do a rotation by 180° (i.e. both horizontal and vertical reflections) then continue with step 1 Note that for 20 pieces this is solvable in 19 swaps, and conversely a 20-piece puzzle can be shuffled using only 19 RNG calls. **Type B:** When swapping two triangles, try each of the following in turn. 1. do a scaling and translation on each triangle as normal to send each outline to the other 2. do a horizontal or vertical reflection on each triangle, then continue with step 1 3. do a transpose or antitranspose (i.e. reflection on one of the 45° diagonals) then continue with step 1. Note that this can be solved by first reducing it to type A, so there is a concern that solving a puzzle like this is more tedious than challenging.