diff --git a/2020/day23/ex1.bash b/2020/day23/ex1.bash
index 742f0c8..e1635a5 100755
--- a/2020/day23/ex1.bash
+++ b/2020/day23/ex1.bash
@@ -6,7 +6,7 @@ CMD=${0##*/}
 shopt -s extglob
 set -o noglob
 
-declare -A next                                   # next[i] is cup right to i
+declare -A next                                   # next[i] is cup right to i (ring)
 declare -i end runs cup _cup
 
 read -r str
@@ -27,9 +27,8 @@ done
 next[$_cup]=$cup                                  # close the ring
 
 _cup=$cup
-
 declare -i _1st _2nd _3rd dest
-# make the moves: a simple sub-linked list operation.
+# make the moves: a simple sub linked list operation.
 for ((i = 1; i <= runs; ++i)); do
     _1st="${next[$cup]}"
     _2nd="${next[$_1st]}"
diff --git a/2020/day23/ex2.bash b/2020/day23/ex2.bash
index 5fee486..e9d92e6 100755
--- a/2020/day23/ex2.bash
+++ b/2020/day23/ex2.bash
@@ -33,6 +33,7 @@ next[$_cup]=$cup                                  # close the ring
 
 _cup=$cup
 declare -i _1st _2nd _3rd dest
+# make the moves: a simple sub linked list operation.
 for ((i = 1; i <= runs; ++i)); do
     _1st="${next[$cup]}"
     _2nd="${next[$_1st]}"