A note before the list
The research on brain training games is mixed, so this post makes no promises about your brain. What a good puzzle does is ask for one specific kind of thinking, and you get noticeably better at that kind with practice. Here are five games on GAMEFREEX, what each one asks for, and a technique that helps.
Logic Freex: deduction
What it asks for: filling a grid so that every row and column holds each number once.
The grids go from 4 by 4 to 7 by 7 over eight levels, and there are no boxes, only rows and columns. Every puzzle has exactly one solution. The technique: for each empty cell, list the numbers that are still possible. On a 4 by 4 grid, if a row already has 1 and 3 and the column of one empty cell already has a 2, that cell must be 4. When you feel you have to guess, you have missed a crossing column.
Bomber Freex: reading clues
What it asks for: working out where mines are from the numbers around them.
Two rules solve most of a board. If a 1 touches only one hidden cell, that cell is a mine. If a number already has all its mines flagged, every other hidden cell next to it is safe. Boards grow from 8 by 8 to 20 by 20, and from level two you earn tools such as X-Ray, which reveals a 3 by 3 area safely. Keep those for the spots where the numbers cannot decide.
Memory Freex: holding a sequence
What it asks for: repeating a light sequence on four panels that grows by one step every round.
Name the colors in your head as they flash (pink, cyan, cyan, yellow) and group them in threes or fours, like a phone number. There is no timer on your answer, only on the playback, so take a breath before you start pressing. Each round only adds a step at the end, and you already know everything before it.
Dot Freex: seeing the board
What it asks for: spotting moves that change the board for your next turn.
Lines of one color clear when you release, but closing a loop clears every square of that color on the 6 by 8 grid, for triple points. You start with 30 moves and win five back per level, so loops are what keep a run alive. The technique: clear a different color that sits between two groups of the same color, so they fall together and form a loop next move.
Square Freex: planning space
What it asks for: fitting shapes on a 9 by 9 board without boxing yourself in.
There is no timer and no rotation, and the game ends when nothing in your tray fits. Before placing a piece, check that the other shapes in the tray will still have room afterwards. Keep the center open for large shapes, and remember that a 3 by 3 box often fills faster than a full row.