The al­gorithm goes as fol­lows:

1. Solve the top row.
2. Solve the left column.
3. Re­peat Steps 1 and 2 for each ad­di­tional layer un­til you reach the last 2x2.
4. Solve last 2x2 by pick­ing clock­wise or coun­ter­clock­wise and keep ro­tat­ing un­til fin­ish.
1. This size does not mat­ter which dir­ec­tion guar­an­tee­ing fin­ish in 4 or less full ro­ta­tions.
2. However, in most cases, there is a bet­ter dir­ec­tion to spin but is less im­port­ant than the pre­vi­ous steps.

This al­gorithm works for all dif­fi­culties and has a greater im­pact on the lar­ger boards than on the smal­ler boards. Permalink: this-al­gorithm-works-for-all-dif­fi­culties-and-has-a-greater-im­pact-on-the-lar­ger-boards-than-on-the-smal­ler-boards#

▶︎ Ex­ample Permalink: ex­ample#

The al­gorithm goes as fol­lows:

1. Solve each row up to the 2nd num­ber.
1. Solve top row for 1 and 2.
2. Solve middle row for 4 and 5.
3. Solve bot­tom row for 7 and 8.
2. Move the fi­nal column up or down to fin­ish.

▶︎ Ex­ample Permalink: ex­ample-1#

The al­gorithm goes as fol­lows:

1. Solve each row un­til the last column.
1. Solve first row for 1 2 3 4.
2. Solve second row for 6 7 8 9.
3. Con­tinue solv­ing like a and b for the re­main­ing rows.
2. Solve right column with swaps.
1. Find a num­ber in the column that is in the wrong po­s­i­tion.
2. Move the piece into your row left.
3. Move this piece from your row into the cor­rect po­s­i­tion.
4. Re­peat a through c un­til all pieces are in the cor­rect po­s­i­tion.
3. Move the right column un­til up or down un­til solved.

Be care­ful to not end up with a mixed up row (ex: 18 19 15 16) after swap­ping. Permalink: be-care­ful-to-not-end-up-with-a-mixed-up-row-ex-18-19-15-16-after-swap­ping#

▶︎ Ex­ample Permalink: ex­ample-2#

The al­gorithm goes as fol­lows:

1. Solve each row un­til the last column.
1. Solve first row for 1 2 3 4 5.
2. Solve second row for 7 8 9 10 11.
3. Con­tinue solv­ing like a and b for the re­main­ing rows.
2. Solve last column par­ity case.
1. Find a num­ber in the column that is in the wrong po­s­i­tion.
2. Do re­peated swaps of those num­bers by fol­low­ing this.
1. Pick which num­bers you are go­ing to swap.
2. Move the top num­ber into the row next to it.
3. Move the column up to reach the bot­tom num­ber.
4. In­sert the bot­tom num­ber into the row next to the top num­ber.
5. Re­peat ↓ ← ↑ ← un­til num­bers are suc­cess­fully swapped.
3. Re­peat b un­til that num­ber is in the cor­rect po­s­i­tion.
4. Re­peat a through c un­til all num­bers are in the cor­rect po­s­i­tion.
3. Move the last column up or down un­til solved.

▶︎ Ex­ample Permalink: ex­ample-3#

The al­gorithm goes as fol­lows:

1. Solve top row then the middle tap­ping tiles be­low the row.
1. Make the cen­ter tile of a row the same as one edge tile.
2. Make the row all the same num­ber.
3. Solve the row.
2. Solve bot­tom row the same way but us­ing the middle row.
3. Us­ing the top row, fin­ish the solve.

▶︎ Ex­ample Permalink: ex­ample-4#

The al­gorithm goes as fol­lows:

1. Solve the top three rows after an­other tap­ping tiles be­low the row.
1. Make the cen­ter tile the same as its ad­ja­cent edge tile.
2. Make the other cen­ter tile the same as its ad­ja­cent edge tile.
3. Solve the left two tiles by press­ing.
4. Solve the right two tiles by press­ing.
2. Solve the bot­tom row the same way but by us­ing the bot­tom row it­self.
3. Us­ing the first and second row, fin­ish the solve.

Tip: When you solve dur­ing step 2, tap the first row the same num­ber of times as the bot­tom row. You can then use row 2 to fin­ish the solve. Permalink: tip-when-you-solve-dur­ing-step-2-tap-the-first-row-the-same-num­ber-of-times-as-the-bot­tom-row-you-can-then-use-row-2-to-fin­ish-the-solve#

▶︎ Ex­ample Permalink: ex­ample-5#

The al­gorithm goes as fol­lows:

1. Solve the top row by tap­ping tiles dir­ectly be­low the row.
1. Solve the cen­ter tile.
2. Solve the tile to the left of the cen­ter tile.
3. Solve the tile two spaces to the left of the cen­ter tile.
4. Solve the tile three spaces to the left of the cen­ter tile.
5. Re­peat steps b-d but to the right of the cen­ter tile.
The top row should now be en­tirely filled with 1s.
2. Re­peat step 1 for every row un­til the bot­tom row (don't solve the bot­tom row yet).

To verify there is no mis­take: Permalink: to-verify-there-is-no-mis­take#

• When you are done, your board will be sym­met­ric.
• The two tiles ad­ja­cent to the bot­tom cen­ter tile will al­ways be 1 or 4.

▶︎ Ex­ample Permalink: ex­ample-6#

You will want to read how to propag­ate be­fore con­tinu­ing. The al­gorithm goes as fol­lows:

1. Propag­ate.
2. La­bel the bot­tom right cells (from left to right): A, B, C, D. La­bel the top right cells (from left to right): a, b, c, d. We will be tap­ping the top row to en­code the bot­tom row onto it.
   1. Tap a so that a is the same as C.
   2. Tap b and d the num­ber of times you will need to solve C.
   3. Tap a the num­ber of times you would need to solve D.
   4. If B + D is odd, tap c three times (once in Hard). Oth­er­wise, skip this step.
3. Propag­ate from top once more to fin­ish the solve.

▶︎ Ex­ample Permalink: ex­ample-7#

▶︎ Hard Lookup Table Permalink: hard-lookup-table#