(Shutterstock)
(Shutterstock)

The Grump and Widen Show: Weekly Puzzle by Dilip D’Souza

Can you pick the Crazydent from the way the people in the Benighted Plates of Amberica cast their vote?
By By Dilip D’Souza | Hindustan Times
UPDATED ON NOV 13, 2020 06:05 PM IST

The US election is over (I hear you muttering gratefully under your breath). But while it is still on your mind, let me run a thought experiment by you.

In the Benighted Plates of Amberica (BPA), everyone lives in one of two towns: North Plate (NP) and South Plate (SP). For some reason, all of NP’s voters are thought to belong to the Prepubican Party; all of SP voters are thought to belong to the Lameokrat Party.

BPA conducts peculiar elections, in Stages. Only two candidates can run, one from each party. Authorities call in a batch of voters from NP to vote, note which candidate got the most votes, discard the rest and announce the winner and her winning percentage. Then they call in a batch from SP and do the same. The candidate with the higher percentage is the winner of Stage 1. On they go to Stage 2, operating in the same way, and to more Stages as necessary.

The candidate who wins the most Stages becomes the country’s Crazydent. You can pick holes aplenty in this process, but it’s what BPA’s founders, the venerable Pilgrim Platters, spelled out.

In last week’s election for Crazydent, the two candidates were Dough Grump (Prepubican) and Sonal Widen (Lameokrat). Because of a deadly pandemic, there were many fewer voters than usual — only 500 in each town — and so only two Stages to the election.

In Stage 1, 125 NP voters came in. 116 voted for Grump, or 93%. Then 375 SP voters entered; 326 voted for Widen, or 87%. So Grump won Stage 1.

In Stage 2, 274 of 375 NP voters voted for Grump: 73%. As expected, Widen got most of the Stage 2 SP batch’s votes, but less than 73%. So this was a second Grump Stage win — and Grump readied to crown himself Crazydent.

But Widen yelled: “Hey! Wait a minute! I should be Crazydent! Because if you take vote counts, I won more!”

She was right.

Questions: How is this possible? Can you come up with numbers for how the vote went for the second SG batch? And can you explain what happened here?

Scroll down for the solution

.

.

.

.

.

The Weekly Puzzle Solution

This is an example of what mathematicians know as Simpson’s Paradox. A good example is Hilary Clinton losing the Electoral College vote in the 2016 US Presidential election despite winning the popular vote.

In this case, Grump got 390 of 500 NP votes. Widen got more than 390 of 500 SP votes.

An easy way to think of this is that when the larger batch of 375 from each town voted (SP in Stage 1, NP in Stage 2), Widen’s win (87%) was more comprehensive than Grump’s (73%).

To make that even clearer, imagine the election went like this:

Stage 1: 2 NP voters, 2 for Grump, 100%. 498 SP voters, 490 for Widen, 98%. Grump wins Stage 1.

Stage 2: 498 NP voters, 300 for Grump, 60%. 2 SP voters, 1 for Widen, 50%. Grump wins Stage 2.

But Grump actually has only 302/500 votes. Widen: 491/500.

In this puzzle, Widen could have got anywhere between 65 and 91 votes of that Stage 2 SP batch of 125. Then she would have lost Stage 2, but won the overall count.

SHARE THIS ARTICLE ON
app
Close
What’s in store for Aries, Virgo, Libra, Scorpio and other zodiac signs.
What’s in store for Aries, Virgo, Libra, Scorpio and other zodiac signs.

Horoscope Today: Astrological prediction for January 21

By Dr Prem Kumar Sharma, Manisha Koushik
PUBLISHED ON JAN 21, 2021 12:10 AM IST
Daily horoscope: Are the stars lined up in your favour? Find out the astrological prediction for Aries, Leo, Virgo, Libra and other zodiac signs for January 21.
Close
Models in Alessandro Sartori’s creations (Photo: Instagram/Zegna)
Models in Alessandro Sartori’s creations (Photo: Instagram/Zegna)

Sartori’s sartorial sorcery

By Manish Mishra
PUBLISHED ON JAN 20, 2021 09:59 PM IST
Could you picture yourself in a skinny tailored suit post Covid? The pandemic and its cruel aftermath altered the way we engage with clothing as comfort takes precedence over being on trend
Close
Tilda Swinton(Instagram)
Tilda Swinton(Instagram)

Tilda Swinton reveals she identifies as queer

PTI
UPDATED ON JAN 20, 2021 08:10 PM IST
The 60-year-old actor, known for films such as "Orlando", "The Chronicles of Narnia" series, "Okja" and "Suspiria", said being queer is a "sensibility" for her.
Close
Kamala Harris(Instagram)
Kamala Harris(Instagram)

Vogue to release new Kamala Harris cover after controversy

AFP
PUBLISHED ON JAN 20, 2021 07:56 PM IST
Editor Anna Wintour was forced to defend the original image after it circulated online earlier this month, insisting it was not the magazine's intention to "diminish" Harris's "incredible" election victory.
Close
Vice President-elect Kamala Harris' understated and elegant signature style of blazers combined with sneakers signals a new way of power dressing.(Yahoo)
Vice President-elect Kamala Harris' understated and elegant signature style of blazers combined with sneakers signals a new way of power dressing.(Yahoo)

Kamala Harris brings in new style of power dressing with blazers and sneakers

PTI
PUBLISHED ON JAN 20, 2021 06:44 PM IST
Vice President-elect Kamala Harris' understated and elegant signature style of blazers combined with sneakers signals a new way of power dressing.
Close
Priyanka Chopra Jonas(Instagram)
Priyanka Chopra Jonas(Instagram)

Priyanka Chopra Jonas dubs herself 'updo expert', shares glamorous selfie

By hindustantimes.com | Edited by Alfea Jamal
PUBLISHED ON JAN 20, 2021 06:21 PM IST
Bollywood star Priyanka Chopra Jonas on Wednesday treated fans to a glamorous selfie and called herself an "updo expert."
Close
Recipe: Trying to cut out added sugars? Let date balls tame your sweet cravings(Instagram/chroniclesofanewbride)
Recipe: Trying to cut out added sugars? Let date balls tame your sweet cravings(Instagram/chroniclesofanewbride)

Recipe: Trying to cut out added sugars? Let date balls tame your sweet cravings

By Zarafshan Shiraz
UPDATED ON JAN 20, 2021 06:17 PM IST
  • Date amid lockdown? Why not! Except, it’s sweeter, healthier, doesn't give you anxiety and one that even your parents will not refuse. Don’t believe us? Check out this winter special recipe of coconut date balls that only require four ingredients and thank us later
Close
The Seychelles government has opened the country for tourism for those who have taken both the doses of Covid-19 vaccine and have a negative report from a RT-PCR test done 72 hours prior to the journey, said an official statement on Wednesday.(Unsplash)
The Seychelles government has opened the country for tourism for those who have taken both the doses of Covid-19 vaccine and have a negative report from a RT-PCR test done 72 hours prior to the journey, said an official statement on Wednesday.(Unsplash)

Seychelles opens up for tourism for vaccinated travellers

PTI
PUBLISHED ON JAN 20, 2021 05:46 PM IST
The Seychelles government has opened the country for tourism for those who have taken both the doses of Covid-19 vaccine and have a negative report from a RT-PCR test done 72 hours prior to the journey, said an official statement on Wednesday.
Close
The Dutch government is set to add the first nationwide curfew since World War II to its already broad lockdown on Wednesday in a bid to limit the spread of new coronavirus mutations in the Netherlands.(Reuters)
The Dutch government is set to add the first nationwide curfew since World War II to its already broad lockdown on Wednesday in a bid to limit the spread of new coronavirus mutations in the Netherlands.(Reuters)

Dutch government to introduce first curfew since World War II

Reuters
PUBLISHED ON JAN 20, 2021 05:05 PM IST
The Dutch government is set to add the first nationwide curfew since World War II to its already broad lockdown on Wednesday in a bid to limit the spread of new coronavirus mutations in the Netherlands, broadcaster RTL said.
Close
Mandira Bedi has a fun fitness session at home(Instagram/mandirabedi)
Mandira Bedi has a fun fitness session at home(Instagram/mandirabedi)

Watch: Mandira Bedi is ready to exercise jaise bhi kaise bhi, even on trampoline

By Nishtha Grover, Delhi
PUBLISHED ON JAN 20, 2021 05:04 PM IST
Fitness enthusiast Mandira Bedi recently shared a fun fitness video that was shot by her son and shows the actor jumping on a trampoline while working out.
Close
Burberry (Instagram)
Burberry (Instagram)

Burberry sales drop as new coronavirus lockdowns keep shoppers home

Bloomberg
PUBLISHED ON JAN 20, 2021 04:52 PM IST
The update shows how 2020 kept challenging luxury companies with on-off policies that closed, then opened and then closed retailers again from October in many European countries.
Close
Want to get your stamina back post Covid? Check out Varun Dhawan’s fitness video(Instagram/varundvn)
Want to get your stamina back post Covid? Check out Varun Dhawan’s fitness video(Instagram/varundvn)

Want to get your stamina back post Covid? Check out Varun Dhawan’s fitness video

By Zarafshan Shiraz
UPDATED ON JAN 20, 2021 04:28 PM IST
  • From right side lateral travelling ape to full scorpion, here’s how Coolie No.1 star Varun Dhawan recovered and got his stamina back after suffering from Covid-19 | Watch
Close
A study published in journal Human Gene Therapy shows that gene editing therapies, including CRISPR-Cas frameworks, offer the possibility to address transformations causing inherited retinal degenerations, a leading cause of blindness.(ANI)
A study published in journal Human Gene Therapy shows that gene editing therapies, including CRISPR-Cas frameworks, offer the possibility to address transformations causing inherited retinal degenerations, a leading cause of blindness.(ANI)

Study highlights genome altering can help to treat human retinal degeneration

ANI
PUBLISHED ON JAN 20, 2021 03:35 PM IST
A study published in journal Human Gene Therapy shows that gene editing therapies, including CRISPR-Cas frameworks, offer the possibility to address transformations causing inherited retinal degenerations, a leading cause of blindness.
Close
Gauahar Khan looks stunning on honeymoon(Instagram/gauaharkhan)
Gauahar Khan looks stunning on honeymoon(Instagram/gauaharkhan)

Newly-wed Gauahar Khan looks beautiful in makhmal suit on honeymoon with Zaid

By Nishtha Grover, Delhi
PUBLISHED ON JAN 20, 2021 03:31 PM IST
  • Gauahar Khan has been sharing snippets from her honeymoon in Udaipur with hubby Zaid Darbar. However, her fans cannot help but swoon over the stunning outfits that the actor wore on her trip. Her latest images wearing a makhmal suit has been making headlines and we are taking notes.
Close
Representational image(Unsplash)
Representational image(Unsplash)

Loss of smell may be best predictor of Covid-19, research confirms

PTI
PUBLISHED ON JAN 20, 2021 02:48 PM IST
The research found that only around half of patients with a loss of smell got their sense of smell back after forty days.
Close
SHARE
Story Saved
OPEN APP