Problem 44701. Nodal Voltage of Resistor Ladder Network

• You have a bunch (an even number N) of identical resistors (each R ohms), a good battery (V volts) and a high impedance voltmeter.
• Create a ladder network as follows.
• Connect N/2 of the resistors in series to each other (not a loop) giving N/2 + 1 node.
• Connect the node at one end to the positive terminal of the battery and the negative terminal to the ground.
• Connect each of the remaining N/2 nodes to the ground through one resistor from the other N/2 remaining resistors.
• Starting from the node at the battery, use the voltmeter to measure the readings with reference to the ground at each of the N/2 + 1 node.

Note: This problem illustrates an application of Number Theory in circuit analysis.