Solved

Find a number m such that 2m and the square of m have the same digit sum
The number has the property that and have the same digit sum. It is the seventh number, including zero, in the sequence of nu...

15 days ago

Solved

Determine the minimum number of swaps to sort a vector
Cody Problem 1401 asks us to sort a vector with the bubble sort algorithm and count the number of swaps needed. For example, to ...

15 days ago

Solved

Compute flow in a partially full pipe
Problem statement When does the maximum flow occur in a pipe? Intuition might suggest that it occurs when the pipe is flowing f...

15 days ago

Solved

Route a hydrograph through a river section with the Muskingum method
Problem statement Write a function that routes a hydrograph through a river section using the Muskingum method. The input to t...

15 days ago

Solved

Solve an ODE: draining tank
Write a function to compute the time to drain a cylindrical tank of diameter from an initial level to a level . The outflow oc...

15 days ago

Solved

Compute infiltration and runoff under constant precipitation with the Green-Ampt method
Problem statement Write a function that computes infiltration, depression storage, and runoff using the Green-Ampt method. It s...

15 days ago

Solved

Inscribe a circle in a triangle with a side of length equal to the circle’s circumference
A circle of radius is inscribed in a triangle with a side that has a length equal to the circle’s circumference. The center of ...

15 days ago

Solved

Determine whether a hydrograph is a unit hydrograph
A hydrograph describes the runoff response of a catchment or watershed to rainfall. It shows the runoff rate (or flow or discha...

15 days ago

Solved

Compute the average precipitation for a watershed using the Thiessen polygon method
Several methods are available for estimating the average precipitation for a watershed from a few observations at rain gauges. T...

15 days ago

Solved

Compute frequency factors for the normal distribution
In frequency analysis in hydrology, the streamflow corresponding to a specified exceedance probability (or return period ) can...

15 days ago

Solved

Determine flows of given probability using empirical frequency analysis
Write a function that takes as input observations of peak streamflow and exceedance probabilities expressed as percentages an...

15 days ago

Solved

Find patterns in subprime Fibonacci sequences
Lots of Cody problems involve Fibonacci and Collatz sequences. Fibonacci sequences start with two numbers, and later terms are c...

15 days ago

Solved

List unitary divisors of a number
A unitary divisor of a number divides and satisfies gcd(,) = 1. For example, 9 is a unitary divisor of 18 because gcd(9,2) = ...

16 days ago

Solved

List numbers that are not in the Fibonacci sequence
In the list of 4797 Cody problems, 53 deal with or refer to the Fibonacci sequence.* What about the other numbers? Write a funct...

16 days ago

Solved

Determine whether one vector is a subset of another
While bumbling through a pair of problems in the Number Theory group, I wrote code to determine whether a vector is a subset of ...

16 days ago

Solved

Find the length of stream affected by a spill
When a contaminant is spilled into a stream, one might want to know how much of the stream is affected—e.g., the length over whi...

16 days ago

Solved

Count the ways to make Scorigami
Regarding the sport known as American football, some people are such rabid fans that they can tell you the statistics of every p...

16 days ago

Solved

Solve an ODE: concentrations predicted by the cells-in-series model
One approach for predicting mixing and transport of contaminants in a river is the cells-in-series model. The model divides a ri...

16 days ago

Solved

Spell musical triads
Chords form the basis of harmony in music. The most basic chords are triads, or groups of three notes. They are specified by thr...

17 days ago

Solved

Solve an ODE: precocious pair’s porcine pursuit
In our previous encounters with Matilda and Labrun, the scintillating siblings collected candy wrappers, amused others with card...

17 days ago

Solved

Solve an ODE: first-order linear equation
In the fall semester of [redacted], my professor for a course on ordinary differential equations said, “There are two groups of ...

17 days ago

Solved

Solve an ODE: nonlinear third-order equation
Write a function to solve the ordinary differential equation on the domain with , , and either or . The input variable ord ...

17 days ago

Solved

Check whether a Wordle guess is consistent with previous feedback
The game Wordle resembles the classic game Mastermind. Players try to guess a five-letter word, and after each guess they are to...

17 days ago

Solved

Determine whether a player solved a Cody problem
Write a function to determine whether a player has solved the specified Cody problems. The problem numbers are specified as a ve...

17 days ago

Solved

Collect a set of candy wrappers
This past Halloween, the siblings Matilda and Labrun amused (and sometimes confused) their many neighbors with their costumes in...

17 days ago

Solved

Sum of Elements Above the Main Diagonal of a Square Matrix
Given a square matrix as input, write a function that returns the sum of all elements above the main diagonal. If the input mat...

17 days ago

Solved

Multiply binary numbers
Write a function to multiply two binary numbers input as strings. For example, input values of ‘1011’ and ‘101’ should give ’110...

17 days ago

Solved

Pick the die most likely to win
After discussing Rock, Paper, Scissors, Lizard, Spock in The Simpsons and their Mathematical Secrets, Simon Singh writes that in...

17 days ago

Solved

Compute a sum involving the totient over divisors of a number
Write a function to compute the following sum: where is the totient function. The sum is computed over the divisors of (inc...

17 days ago

Solved

Solve an ODE: equation C
Write a function to solve the following ordinary differential equation: with and . The parameter is a constant. The functi...

17 days ago