DIY Challenge 3: Why do the compositions double?
In the previous challenge, many of you have shared a pattern that the Number of compositions is doubling.
The challenge is to explain the reason for the pattern which you observed.
In the following video, I share a systematic way of decomposing numbers, and a hint to why we might be seeing the pattern.
Why are the number of decompositions doubling each time?
What students worked out7
Student 11
Sir I got 17 ways of decomposing 5
Student 2
yeah I am positive that there are only 16 ways
Student 2
Student 4
What is the 17th way of decomposing 5
Student 9
sir it is because all the numbers except 1 are even
and they all are dependent on 1Student 9
Sir we have to add all the numbers before the number you have chosen and then add 1 to it.
For example;-7->64 = (1+2+4+8+16+32)+1Student 3
FOR EXAMPLE 5 CAN BE written in all different ways how we have written earlier numbers 1,2,3,4 and one more way that number itself
so for 5
(1+2+4+8)+1= 16 ways