This is from Sanjoy Mahajan’s The Art of Insight Problem 1.5
Make a tree diagram for your estimate in Problem 1.3. Do it in three steps: (1) Draw the tree without any leaf estimates, (2) estimate the leaf values, and (3) propagate the leaf values upward to the root.
This is referring to the suitcase of money.
Step 1: Tree
graph LR;
VolBankNote[Volume of Bank Note]
VolSuitcase[Volume of Suitcase]
ValueBankNote[Value of Bank Notes in Suitcase]
NumBankNote[Number of Bank Notes in Suitcase]
ValueSuitcase[Value of Suitcase]
NumBankNote --> ValueSuitcase
ValueBankNote --> ValueSuitcase
VolBankNote -->|-1| NumBankNote
VolSuitcase --> NumBankNote
SuitWidth[Width of Suitcase] --> VolSuitcase
SuitHeight[Height of Suitcase] --> VolSuitcase
SuitDepth[Depth of Suitcase] --> VolSuitcase
BankHeight[Height of Bank Note] --> VolBankNote
BankWidth[Width of Bank Note] --> VolBankNote
BankDepth[Thickness of Bank Note] --> VolBankNote
Step 2: Annotated Leaves
graph LR;
VolBankNote[Volume of Bank Note]
VolSuitcase[Volume of Suitcase]
ValueBankNote[Value of Bank Notes in Suitcase<br>$100]
NumBankNote[Number of Bank Notes in Suitcase]
ValueSuitcase[Value of Suitcase]
NumBankNote --> ValueSuitcase
ValueBankNote --> ValueSuitcase
VolBankNote -->|-1| NumBankNote
VolSuitcase --> NumBankNote
SuitWidth[Width of Suitcase<br/>30cm] --> VolSuitcase
SuitHeight[Height of Suitcase<br/>50cm] --> VolSuitcase
SuitDepth[Depth of Suitcase<br/>30cm] --> VolSuitcase
BankHeight[Height of Bank Note<br/>15cm] --> VolBankNote
BankWidth[Width of Bank Note<br/>6cm] --> VolBankNote
BankDepth[Thickness of Bank Note<br/>0.01cm] --> VolBankNote
Step 3: Propagate
graph LR;
VolBankNote[Volume of Bank Note<br>1 cm<sup>3</sup>]
VolSuitcase[Volume of Suitcase<br>50L]
ValueBankNote[Value of Bank Notes in Suitcase<br>$100]
NumBankNote[Number of Bank Notes in Suitcase<br>50,000]
ValueSuitcase[Value of Suitcase<br>$5 Million]
NumBankNote --> ValueSuitcase
ValueBankNote --> ValueSuitcase
VolBankNote -->|-1| NumBankNote
VolSuitcase --> NumBankNote
SuitWidth[Width of Suitcase<br/>30cm] --> VolSuitcase
SuitHeight[Height of Suitcase<br/>50cm] --> VolSuitcase
SuitDepth[Depth of Suitcase<br/>30cm] --> VolSuitcase
BankHeight[Height of Bank Note<br/>15cm] --> VolBankNote
BankWidth[Width of Bank Note<br/>6cm] --> VolBankNote
BankDepth[Thickness of Bank Note<br/>0.01cm] --> VolBankNote