What was the puzzle?
Initially the 6 people are lined up on the 7 stones from left to right as follows:
Ann Ben Jen EMP Tim Jim Kim
(where EMP stands for empty stone).
Step 1: Tim jumps to occupy the empty stone.
Ann Ben Jen Tim EMP Jim Kim
Step 2: Tim helps Jen in occupying the newly emptied stone between him and Jim.
Ann Ben EMP Tim Jen Jim Kim
Step 3: Ben occupies the stone emptied by Jen.
Ann EMP Ben Tim Jen Jim Kim
Step 4: Ben helps Tim in occupying the newly emptied stone.
Ann Tim Ben EMP Jen Jim Kim
Step 5: Jen helps Jim in occupying the empty stone.
Ann Tim Ben Jim Jen EMP Kim
Step 6: Kim occupies the stone emptied by Jim.
Ann Tim Ben Jim Jen Kim EMP
Step 7: Kim helps Jen in occupying the stone vacated by her.
Ann Tim Ben Jim EMP Kim Jen
Step 8: Jim helps Ben in occupying the stone vacated by Jen.
Ann Tim EMP Jim Ben Kim Jen
Step 9: Tim helps Ann in occupying the empty stone.
EMP Tim Ann Jim Ben Kim Jen
Step 10: Tim jumps to the stone emptied by Ann.
Tim EMP Ann Jim Ben Kim Jen
Step 11: Ann helps Jim in occupying the stone vacated by Tim.
Tim Jim Ann EMP Ben Kim Jen
Step 12: Ben helps Kim in occupying the stone vacated by Jim.
Tim Jim Ann Kim Ben EMP Jen
Step 13: Ben occupies the empty stone.
Tim Jim Ann Kim EMP Ben Jen
Step 14: Kim helps Ann in occupying the stone emptied by Ben.
Tim Jim EMP Kim Ann Ben Jen
Step 15: Kim jumps to the stone emptied by Ann.
Tim Jim Kim EMP Ann Ben Jen
This is exactly what we wanted!