Light the lights again: solution for 7035
Harry: At first when solving the problem we used 100 square which we coloured in when testing numbers to find patterns. We started testing the numbers starting at one and coloured in the hundred square based on what colour lights lit up.
Eve: We decided to test even numbers first and we quickly realised for all even numbers one of the lights was always green. We tested more even numbers and each proved our theory. All even numbers=green.
Caleb: We then decided to test blue. We realised 1 was blue, then 4 and then 9. We started to write the list of blue numbers and realised they were square numbers. We tested this using our knowledge of square numbers and each time the blue light lit up. All square numbers=blue.
Harry: Then we decided to focus on red we knew 1 was red and we tested all numbers increasing by 1 until 6 turned red. We wondered if every number that ended with 1 and 6 was red. We tried 11 and 16 then 21 and 26 and all of them were red. To make sure we were right we checked other numbers that didn’t end in 1 and 6 such as 19. All numbers ending in a 1 or 6= red.
Eve: We found yellow the most challenging, we used trail and error for numbers 1-10 and we found 1, 3, 6 and 10 lit up yellow. We looked carefully at 1, 3, 6 and 10 and figured out the difference between each number increased by one each time, for example 1-3 there is one number in between, 3-6 there is two numbers in between and 6-10 there are three numbers in between. To prove our theory we kept adding 1 more to the difference each time and found 15 and 21 lit up. We checked this for the rest of our 100 square and beyond even 105 was yellow proving our theory. When starting at 1 the difference between yellow numbers increases by 1 each time= yellow.