DIY Challenge 3: Four disks, built from three

You have already solved the problem for 3 disks in the previous challenge.

Can you write the steps needed for 4 disks in a simple way using your solution of 3 disks challenge.

What students worked out5

Student 22021-01-14
make purple/blue/green 1 big block{X}
move it to b (total 7 moves)
move yellow to c
move X to c
3 moves X(b)-yellow(c)-X(c)
so total 15 moves
Student 12021-01-17
I will tell in class I got it in 15 moves
Student 32021-01-17
FIRST DO SEVEN STEPS AS IN 3 DISK PROBLEM. BUT HERE YOU COMPLETE IN TOWER ‘B’
TRANSFER 4TH RING IN TOWER C AND THEN AGAIN DO SEVEN STEPS
SO 7+1+7= 15 STEPS NEEDED
Student 42021-01-17
do moves for three disks but finish in peg b
green-peg c
do moves for 3 disks again and complete in peg c
Student 102021-01-17
First, do all the 7 steps with 3 disks, but instead of stacking them in Peg C, stack them in Peg B. Then transfer the biggest ring from Peg A to Peg C and again do the 7 steps to complete the problem.
Therefore, steps required = 7+1+7 = 15 Steps