156740

For the first part, I originally began sorting the cards in a random order yet got no luck from this. So I devised a way to try and find at least 1 solution for it. I began by putting the largest number on the outermost side and positioned the other 2 numbers inside of the sandwich. The formation was:3,1,2,1,3,2. Then I began to see if putting the other 2 numbers (1 and 2) on the outside would also make all 3 fit in if I arranged them correctly. So I tried it with the 1 but it didn't work, then I tried it with the 2 on the outside and it was completed in the formation: 2,3,1,2,1,3. I then moved onto 4 and tried the same thing. So 4 went on the outside and I positioned the rest of the cards inside it. I came up with the formation: 4,1,3,1,2,4,3. I moved on to see if I could find any more solutions using this method but I had no luck. I finally moved on to the final challenge, the sandwich going up to number 7. One method had already been found which started with the number 7,the highest number, as I have previously mentioned, is what the other solutions have started with. The formation of the numbers was:7,1,3,1,6,4,3,5,7,2,4,6,2,5. I went on to try to see if there was another solution to this problem but after much debate with myself and a lot of tries using my method, found no other solutions to this problem. Another similarity between the 3 problems, is after the highest number in which all the problems began with, it was followed by 1 which is the lowest number. This is my solution to the NRICH number sandwiches problem.