Hadn't heard of this challenge before. $1.49 a day is what I've actually spent on food for each person in my family of five all this year so far. Now I cheated a little bit because in March and April I barely bought any food and ate down our food supply in the freezer and pantry before the move.
My regular budget is $2 a day per person and that's the rate I was spending when I bought the food we ate from the freezer and pantry. I buy plenty of extras with that budget. The kids have good ice cream every day. I buy the best beef hot dogs. I make chicken nuggets for them with real chicken. We drink a ton of coffee. The baby and I drink almond milk instead of cheaper cow's milk. I buy natural peanut butter, wheat bread and just fruit jelly and we go through a lot of it. I even buy a treat or two every week like soda for pizza night, ice cream novelties(Magnum bars are so good!)and chips. That budget also includes a fast food meal once a month. So I know I could cut out the extras, or use close nutritional alternatives to our preferred foods(frozen broccoli instead of salad for example), and get down to $1.50 a day fairly easily.
The big secrets are to limit variety of ingredients to those you can acquire frugally(we still get a lot of variety in actual finished meals though), stock up when you find low prices, limit portion sizes to what is appropriate for caloric needs, make as much as you can from scratch and don't waste food. I save everything leftover for next day's lunch. If it isn't eaten then I throw it in the freezer as an ingredient for a future meal.