Radcliffe

# This Python script generates a directed graph with
# vertex set V = {0, 1, 2, ..., m-1} and edge set
# E = {(n, f(n)) : n in V} where f(n) = n*n + c (mod m).
#
# Requires the python-igraph package (http://igraph.org/python/)
#
# Author: David Radcliffe (14 February 2014)
# Based on an idea of James Tanton
# https://twitter.com/jamestanton/status/549558473868849152
#

Radcliffe

# Python script to list the titles and running times of the videos
# in a YouTube playlist.
# Note: Only works for up to 100 videos. TODO: Fix this bug.

# The playlist id can be found in the playlist's URL. 
playlist_id = "PLt5AfwLFPxWLNZRKWlcRmTABh_SExiiCj"

from lxml import html
import requests

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ZIP Code,County
55001,Washington County
55003,Washington County
55005,Anoka County
55010,Dakota County
55011,Anoka County
55014,Anoka County
55016,Washington County
55020,Scott County
55024,Dakota County

Radcliffe

from math import log, sqrt, pi, e
from scipy.special import lambertw
fomm numpy import real

# http://mathforum.org/kb/message.jspa?messageID=342551&tstart=0
def invfactorial(n):
    """ Approximate inverse factorial"""
    L = log((x + .036534) / sqrt(2*pi))
    return real(L/W(L/e) - .5)
    

Radcliffe

"""
Problem:

    Arrange the numbers from 1 to m*n in an m-by-n grid so that
    no two consecutive numbers are placed in adjacent cells.
    In how many ways can this be done? Two squares are considered
    touching if they share a corner.

Example:

Radcliffe

"""
James Tanton @jamestanton asked:
Is there a power of three whose digits can be rearranged to form 
another power of three?
(https://twitter.com/jamestanton/status/676773021223272448)

The following Python script searches for examples. There is no power
of three, less than 3^200000, whose digits can be rearranged to form
another power of three.
"""

Radcliffe

"""
Euler's four square theorem states that
  (x1^2 + x2^2 + x3^2 + x4^2) * 
  (y1^2 + y2^2 + y3^2 + y4^2) =
  z1^2 + z2^2 + z3^2 + z4^2, 

where

  z1 = x1*y1 + x2*y2 + x3*y3 + x4*y4
  z2 = x1*y2 - x2*y1 - x3*y4 + x4*y3

Radcliffe

library(dplyr)

d <- read.csv('expenditures.csv')
cats <- unique(d$ProgramCategory)
newnames <- gsub("[- ]", "", cats)

e <- d %>%
  filter(ProgramCategory == cats[1]) %>% 
  select(Year:StudentsServed)

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Radcliffe

"""
Problem M379, Crux Mathematicorum

Proposed by John Grant McLoughlin, University of New Brunswkci,
Fredericton, NB.

The integers 27+C, 555+C, and 1371+C are all perfect squares, the square
roots of which form an arithmetic sequence. Determine all possible values
of C.
"""