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How to gain weight from eating almost exclusively bread and potatoes?
The biggest thing you can do is to make the food you eat more enjoyable and eat more of it. I would have no appetite and starve if i had to eat your diet. The good news is that it's possible to eat a lot better, but still very cheaply. Also you really need to eat two or preferably three or even four meals daily if you want to gain weight.
I would remove eggs and cheese as they aren't a good value. Add black beans, chickpeas, and lentils, which are good over rice (very cheap, especially if you buy them dry in bulk). Pasta too. Add spices, cheap hot sauce, tomato sauce, etc and it becomes a good meal. Try oatmeal for breakfast too. I would also make sure that you are getting as many fruits and vegetables as possible (apples, bananas, carrots, lettuce, broccoli, etc. not too expensive but will complete the meals and provide good nutrition). Also consider pan frying the potatoes - it's tastier than boiling.