Probability Tree Hide Nodes Hide randomly I am creating a probability tree diagram such as
       1
     /   \
   .4    .6
  / \    / \
.2  .2 .2  .4

The number of nodes and size of the splits is generated randomly based on some conditions.
Now I want to hide the value of some of the nodes. I want to show some and I want the user to find the rest. How can I achieve this? Is there any logic/algorithm to determine this? The logic should work regardless of the size of the tree.  For example, the above could become
       ?
     /   \
   .4     ?
  / \    / \
 ?  .2  ?  .4

I am looking for any predefined algorithm for node value hiding logic in a probability tree.
 A: If you want users to be able to solve for the missing values at level $L-1$, where $L$ is the length of the tree, you can only hide at most $1$ child node of each of the parent nodes on level $L-1$. If that is the case, your algorithm is simple and just generates for each node $i$ at level $L$ a uniform random variable between $1$ and $N(i)$, where $N(i)$ is the number of child nodes of $i$, and hides the corresponding child.
A: Start with the entire tree.  In each row, remove one of each pair of leaves (chosen arbitrarily).  Remove the root (assuming you specify that the tree is a probability tree).  Now, whenever a value has an unknown as its child, you can switch which is unknown.  Repeat this process until you get bored.
This will give a tree that can be solved to find the original tree.  I can’t prove that all such solvable trees can be made this way.
A: You can do this recursively with the following procedure:
There are two kinds of nodes: 'bottom up' (B) and 'top down' (T) nodes. B nodes should be calculated by adding up values of their children or their value is shown. T nodes should be calculated as the value of their parent minus the value of their sibling. The root node is a T node, since its value is known to be $1$, but still can be hidden.
For each B node, decide whether or not its value will be shown. If it is shown, make one child a T node and one child a B node. Else, make both childs B nodes. (If B has no children, its value must be shown.)
For each T node, do not show its value. Make one child a T node and one child a B node. If the node has no children, hide its value.
