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Solving mathematical puzzles can be fun, but you may find them hard at first. In what follows, you will find strategies that can help you solve these puzzles. Have a quick look:

- Always set the aim to win.
- Find out what is considered a win.
- Try out the puzzle to get a feel of the game.
- See the big picture of the game.
- After a couple of failures, take a break, minimize distractions, and try again.

# Always set the aim to win.

When you first see a puzzle, you may be intimidated by the complexity of the game, with many arrows going in all directions and numbers sprinkled all over. Don’t panic. Once a puzzle has a solution, you are guaranteed to find it if you work hard enough. So, when you see that puzzle, set yourself to solve it. It does not matter that you have not yet tried it. All you need to think about is finding the solution.

If you cannot erase from your mind that you will never solve this puzzle, take some time to breathe to calm down and ask yourself: “is it really that hard that I cannot solve it?”. You now have set yourself a challenge, and the next move is to understand the puzzle.

# Find out what is considered a win.

To solve a puzzle, you will need to ensure some rules are satisfied. These usually are conditions that guarantee a solution. For example, a puzzle with nodes, arrows, and numbers on the arrows may require you to shuffle the numbers on the arrows until the numbers on all the arrows that enter each node are less than all the numbers on the arrows that exit that node.

If the rules are unclear at first, read them again, and slowly. If they are still unclear after several readings, have someone else read them to check if they understand them. You can also check online to see if other people have understood the conditions or if they have also been confused. If you are convinced that the conditions are confusing, try to contact the puzzle maker for a discussion.

At this point of trying to understand the rules of the game, it is fine if you feel you are in the dark, particularly if you have never played a similar game. At this stage, it is best to consider yourself in learning mode.

# Try out the puzzle to get a feel of the game.

© XY 2021

A mathematical puzzle. To win, you need to shuffle the numbers on the arrows so that for any two arrows that touch a common letter node, the number on the arrow that enters that node must be less than the number on the arrow that exits that node. To shuffle two numbers, you click or tap on one number and then click or tap on the other. Give it a try. © XY 2021

Once you know the rules, try out the puzzle. Go as slowly as you wish so that you can make sense out of the game. During this stage, you will be able to answer questions such as: Is it worth my time and energy? Is it fun? Is it as hard as I wanted it to be?

Take as much time as you want. The more time you take to explore the game the more you are likely to get from the experience in the future. If you feel like setting it aside for some time and then come back to it later, go for it.

If the puzzle is online, you may be able to solve it on both your computer and your mobile phone. Try out both ways to see if there is any difference, and choose the method that suits you the best.

# See the big picture of the game.

If you decide to solve the puzzle, try to understand what the ultimate goal is. For example, if a puzzle requires you to shuffle numbers on arrows, think about how the puzzle will look when you finish solving it. This will help you stay focused because you will know to continue playing as long as you have not reached that goal.

You may have this general idea of the game by reading and understanding the rules, by imagining what will happen when a solution is found, or by slowly trying out the puzzle and seeing a partial solution.

Seeing that big picture may help you decide if you really want to invest any more energy in finding a solution.

# After a couple of failures, take a break, minimize distractions, and try again.

You may find solving a puzzle hard after the first few attempts. A reason is that you may still be in learning mode. If you have never played a similar game before, you will need some time to get used to it.

If you feel you are getting frustrated because of these first failures, take a break. At that point, you may be fatigued by the mental effort you have exerted at trying to solve the puzzle. During the break, take a rest and relax; avoid starting another mentally demanding activity, which could cause more fatigue.

Another reason why you might not be able to solve the puzzle is that you have been too distracted. If you were listening to music, turn it off; if you were texting, stop it, at least for the moment; if you were in a noisy place, move to a quieter place; if you were working out, finish the workout then go back to the game; or if you are preoccupied by other thoughts, then take a break from the puzzle.

Once you have taken care of all these distractions, try solving the puzzle again. You may be surprised at how good you have become at it!

# Last Words

When you combine any of these strategies, you may find that puzzles you thought were unbeatable have become manageable. After all, the more of them you solve, the better you will become at them. If you want to try out more puzzles, try to solve **these ones**.

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