Publications by Jason Shaw
Death by Quarters Solution - Contingencies Mar/Apr 2023 Puzzle
As per the column, we can assume the two racers have equally likely chances of winning each quarter mile lap around the track. Problem 1 What is the probability that Doc and Hoss would end up tied after running 50 races against each other? As it doesn’t matter which order that Hoss wins 25 and that Doc wins 25, this is a simple binomial proba...
2264 sym
A Toddler Eats an Apple
The Problem A certain 2-year-old is eating his favorite snack: an apple. But he eats it in a very particular way. When he first receives the apple, and every minute thereafter, he rotates the apple to a random position and then looks down. If there’s any skin of the apple left in the spot where he plans to take a bite, then he will indeed take ...
4045 sym R (2138 sym/19 pcs) 2 img
GOAT Monty Hall
The Problem Statement From the Riddler: Now suppose Monty changes the rules. First, he will randomly pick a number of goats to put behind the doors: zero, one, two or three, each with a 25 percent chance. After the number of goats is chosen, they are assigned to the doors at random, and each door has at most one goat. Any doors that don’t have ...
3962 sym R (1548 sym/8 pcs)
Catching T-Shirts
Riddler Express Problem 4/10/2020 During a break at a music festival, the crew is launching T-shirts into the audience using a T-shirt cannon. And you’re in luck - your seat happens to be in the line of flight for one of the T-shirts! In other words, if the cannon is strong enough and the shirt is launched at the right angle, it will land in yo...
5463 sym R (2561 sym/7 pcs)
Palindromes and Ambiguous Absolutes
How Many More Palindrome Dates Will There Be This Century? Super Bowl Sunday, when the Chiefs came back from a 10 point deficit in the 4th quarter to defeat the 49ers 31-20, was also a palindrome day. Since we Westerners write the date in the format mm/dd/yyyy, we could have turned that around and had the same day as 02022020 is the same forward ...
2451 sym R (5765 sym/38 pcs)
Extra Points and Delirious Ducks
Extra Point Conversion (Riddler Express) For convenience, the problem statement is given below. The Riddler Football League (RFL) playoffs are upon us! As the coach, you’ve devised a new strategy for scoring after a touchdown. Your team will line up 2 yards away from the goal line in such a way that it could attempt either a 1-point conversion ...
10320 sym R (8128 sym/62 pcs) 6 img
Riddler Spelling Bee
Problem Statement from the Riddler The New York Times recently launched some new word puzzles, one of which is Spelling Bee. In this game, seven letters are arranged in a honeycomb lattice, with one letter in the center. The goal is to identify as many words that meet the following criteria: The word must be at least four letters long. The word ...
2988 sym R (4298 sym/21 pcs)
Chess Match & Prismatic Problem
Chess Match To find this probability we only focus what will happen when one of the two eventually win. On the next game that one of the two wins, the probability that it will be Kasparov is 3/8. This is found using conditional probability. On the next three games on which one of the two win, it must be Kasparov if he is going to win the round. T...
1410 sym R (1367 sym/4 pcs)
Hospital Readmission Solution
This chunk reads in the data, relevels factors, and prints a summary. # Loading data readmission <- read.csv(file="readmission.csv") vars <- colnames(readmission)[c(2,3,5,9)] #variables to relevel for (i in vars){ table <- as.data.frame(table(readmission[,i])) max <- which.max(table[,2]) level.name <- as.character(table[max,1]) re...
4071 sym R (74118 sym/155 pcs) 12 img
Riddle 199 Lottery
World Series Home Team Losing Streaks According to the Riddler, “the home team actually wins about 54 percent of the time in baseball.” Using this, and assuming independent games, we can calculate that the probability of the home team losing 7 games in a row is .004358, or about 1 in 229 chances. p7 <- (0.46)^7 p7 ## [1] 0.004358177 trunc(1...
3003 sym R (2435 sym/45 pcs)