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Here's a set of polyominoes (sizes 4,5,6,7,8,9,10) that you can print and cut out. You can use the two smallest to make a 3x3. Nice easy one to get you started. Add a piece to make a 3x5. Add another to make an 11x2. Then a 5x6, 3x13 and finally a 7x7.

There's only one way to make each rectangle. You are allowed to flip pieces over.

This should be relatively easy to do by hand in a few minutes. A computer would do them all in a split second... and spoil the fun for you.

Polyominoes size 4 through 10

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    $\begingroup$ 11 X 22 is a typo? You need more pieces to make 11 X 22/ $\endgroup$ – Jamal Senjaya Jan 5 '18 at 5:00
  • $\begingroup$ @Jamal Senjaya It should be 11x2 $\endgroup$ – Jay Jan 5 '18 at 5:02
  • $\begingroup$ Thanks I'll fix it...ah never mind already fixed for me! $\endgroup$ – theonetruepath Jan 5 '18 at 6:17
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Looks like prog_SAHIL left the job unfinished, so I'll continue.

This is a really pleasant puzzle, and you really should try it yourself. If you're stuck at the beginning, just remember that

at each phase, you can calculate exactly which pieces you should use.

or more specifically,

For each puzzle, you use the pieces in the previous puzzle, plus the smallest possible new one.

Here are the solutions:

3x3

enter image description here

5x3

enter image description here

11x2

enter image description here

6x5

enter image description here

13x3

enter image description here

7x7

enter image description here

As a note to myself (and anyone else wanting to make reasonably clean looking block puzzle images), here's the method I used for the newest version of the 7x7 solution. If you want to play with the pieces, you should create each of them on a new layer. Since I already had a solution in mind, I only wanted the final image, and made everything on a single layer.

  1. Create a new image in Gimp. (I also opened OPs image, so I could use the eye dropper to pick the colours)
  2. Filters->Render->Pattern->Grid. Choose any grid size you want, but make sure to use 2 as the line width.
  3. Solve the puzzle using the paint bucket tool
  4. Make the grid disappear (I just used the paint bucket to fill the grid with the background colour. If you used layers, just hide the layer with the grid.)
  5. Use the select-by-color tool to select all squares of one block
  6. Select->Grow, and grow the selection by 1. (This is why the grid lines needed to be 2 pixels thick. Now the piece shape is nicely selected.)
  7. Paint the piece solid (since the selection is active, just paint with a large brush)
  8. Change the colour to black, and Edit -> Stroke Selection (line width 2, antialiasing off) to make the outlines.
  9. Repeat for each piece.

Apart from the 7x7, the other solutions still look a bit shabby around the edges, but since they are quite serviceable, the effort to redo them seems a bit too much.

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  • $\begingroup$ I had my school. :p Well thanks for finishing up. $\endgroup$ – prog_SAHIL Jan 5 '18 at 11:11
  • $\begingroup$ Plus I was too lazy to print them at the time. $\endgroup$ – prog_SAHIL Jan 5 '18 at 11:13
  • $\begingroup$ I completed them too. :) $\endgroup$ – prog_SAHIL Jan 5 '18 at 11:30
  • $\begingroup$ @prog_SAHIL yeah, printing is way too much trouble. By the way, I think I finally figured out how to make the figures look halfway decent. I'll update the 7x7 solution and add a note on the method. $\endgroup$ – Bass Jan 5 '18 at 11:35
  • $\begingroup$ Outlines and the note makes it far more better. :) $\endgroup$ – prog_SAHIL Jan 5 '18 at 11:57
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Solved Here!

Full Answer:

1.) 3x3

enter image description here

2.) 3x5

enter image description here

3.) 11x2

enter image description here

4.) 5x6

enter image description here

EDIT: Bass submitted the other two before me, But still I will add them to complete my answer.

5.) 13x3

enter image description here

6.) 7x7

enter image description here

Method:

  • Choosing Pieces

  • 3x3 will have 9 square units, therefore pieces with 4 and 5 square units will be used.
    3x5 will have 15 square units, therefore pieces with 4,5 and 6 square units will be used so on...

  • Forming the shapes

  • Although there is no general rule. But in most of the cases, pieces that need to used as a base can be found , for example, in the 7x7 , the 10 square unit piece will be used as base because only that piece has 7 pieces in a row. Rest of the pieces can be easily accumulated on the base.
    Similarly, 6 square unit piece is used as base in 3x5.
    7 square unit piece is used as base in 5x6.

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    Here is the answer rendered by my program, just for completeness.

    Solution

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