Surviving in the Mountains will probably give you a good shot at surviving the Zombie Apocalypse. They are mostly scarcely populated and have plenty of resources to live from. I will go through the advantages and disadvantages of living in the mountains.
Advantages of surviving in the mountains
As is said the mountains are scarcely populated areas and will have little people and Zombies. The threat of Zombies walking into the mountains is minimal, because Zombies always take the road of minimal resistance, meaning: downwards, unless they have a reason to take on a different road. Furthermore: if you are in steep mountain areas it might be that You will already have trouble climbing it. Imagine a Zombie trying to climb a steep rocky area. It will most likely not succeed. So the mountains will be relatively safe.
Being high up in the mountains gives you a great view what is happening around you. You can see hordes of Zombies coming from afar and maybe spot other survivors down the mountain. Keep in mind that Zombies will be able to see you as well. Keep a low profile and don’t make any light during the night. This will give the Zombies enough reason to climb up the mountain to come and eat you. The best kind of mountain you would want to have are Alpine meadows. Alpine meadows are great for keeping animals and agriculture.
Water will also be no problem. Most likely there is a river from melting ice down the slope. Or there could be ice which you can melt and drink as fresh water. Most of the time there are forests in the mountains from which you can get food, wood and other resources. Further up in the rocky areas are many more useful resources.
Wildlife will also be richly available, if you are lucky there will be herds of sheep or goats on the meadows. Don’t try to kill them, catch them and put them in a large area surrounded by a strong fence. These animals will keep you fed and alive for a long time, so protect them at all cost. Try to keep fortifying these fences so that if a Zombie were to reach your camp, he will need a long time to reach your sheep so you can dispose of him quickly.
There is also a possibility that there are smaller settlements up in the mountains which will have stayed clean from the Apocalypse. This could mean that there is a safe community from which you can rebuild and live peacefully. A community like this is most of the time self sustaining and can easily be upgraded into a strong base using the natural resources. Be sure to check out what kind of people live in the settlement before exposing yourself as you should always do when encountering survivors. They could be raiders so be cautious.
Disadvantages of surviving in the mountains
If there is a mountain next to a large city or settlement the chances will be that its inhabitants will flee into the mountains for the reasons listed above. This is will cause a great threat, because many Zombies will and follow these fleeing people and lure them in the mountains. This could pose a great threat when trying to survive. Always try to go to a mountain far away from civilization.
In all of the world it will be hard to find guns in the scarcely populated areas in the mountains unless there is an army base in the mountains which will be stacked with guns. This could be an advantage as well as a disadvantage. A gun is great for protection, but will lure many Zombies towards you, because sounds travels far in the mountains. Also when encountering other survivors in the mountains, if both survivors do not have a gun they are more likely to work together to survive. They will be on equal terms.
It could be very cold in the mountains so make sure you create a well isolated base. Remember to not have any fires at night, because this will attract many Zombies. Instead you could make some kind of shelter and try to catch sheep or goats. These animals will breathe out warm air, so if you have enough animals in your shelter it will get warmer. They might stink a little, but it is better to stink then to turn into a zombie.
Wildlife can be hunted, but it can also hunt you. Watch out for bears, mountain lions etc. This however depends on where you decide to survive. If you do manage to kill one they can be a valuable resource. They fur is warm as clothes or blankets. And make you look bad ass of course.
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