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
Tree Diagram Bills
insight
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
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