# Tree Diagram Bills

insight
Published

September 29, 2020

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

```