first puzzle : Nonogram
Nonograms, also known as Hanjie, Paint by Numbers, or Griddlers, are picture logic puzzles in which cells in a grid have to be colored or left blank according to numbers given at the side of the grid to reveal a hidden picture. In this puzzle type, the numbers measure how many unbroken lines of filled-in squares there are in any given row or column. For example, a clue of "4 8 3" would mean there are sets of four, eight, and three filled squares, in that order, with at least one blank square between successive groups.
second puzzle : Pentamino
A standard pentomino puzzle is to tile a rectangular box with the pentominoes, i.e. cover it without overlap and without gaps. Each of the 12 pentominoes has an area of 5 unit squares, so the box must have an area of 60 units. Possible sizes are 6×10, 5×12, 4×15 and 3×20. The avid puzzler can probably solve these problems by hand within a few hours. A more challenging task, typically requiring a computer search, is to count the total number of solutions in each case.
The 6×10 case was first solved in 1960 by Colin Brian and Jenifer Haselgrove. There are exactly 2339 solutions, excluding trivial variations obtained by rotation and reflection of the whole rectangle, but including rotation and reflection of a subset of pentominoes (which sometimes provides an additional solution in a simple way). The 5×12 box has 1010 solutions,
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