It's always happy at the banana stand

Logic Level 1

Sandip, Tracy, Jamal, and Sheng are best friends who work together everyday at a banana stand. Since they are so close, their happiness on any given day depends on the happiness of the other three people on the previous day. Suppose they behave as follows:

Sheng is happy today only if Tracy and Jamal were both happy yesterday.
Jamal is happy today only if Sandip or Sheng (or both) were happy yesterday.
Sandip enjoys watching Sheng cry, so Sandip is happy today only if Sheng was sad yesterday.
Tracy is happy today only if Tracy was happy yesterday, meaning she has an independent streak.

Suppose that on day 1, all four of the friends are sad. After a few days, the friends reach a stable emotional state that repeats itself. What is the emotional state of each person in this repeating state?

Sandip: Sad, Sheng: Sad, Jamal: Sad, Tracy: Happy Sandip: Happy, Sheng: Happy, Jamal: Sad, Tracy: Sad Sandip: Happy, Sheng: Sad, Jamal: Happy, Tracy: Sad Sandip: Happy, Sheng: Sad, Jamal: Sad, Tracy: Happy

12 solutions

John M.
Jul 4, 2014

Look at the diagram:

Day 1.

Tracy: Sad

Sheng: Sad

Sandip: Sad

Jamal: Sad

Day 2.

Tracy: Sad

Sheng: Sad

Sandip: Happy [because Sheng was sad yesterday]

Jamal: Sad

Day 3.

Tracy: Sad

Sheng: Sad

Sandip: Happy

Jamal: Happy [because Sandip was happy yesterday]

Day 4 and on:

Tracy: Sad

Sheng: Sad

Sandip: Happy

Jamal: Happy

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Tracy always remains sad. Sheng never becomes happy because Tracy never becomes happy. Sandip remains happy because Sheng remains sad. Jamal remains happy because Sandip remains happy.

Lots of drama ;)

Seeing as Sandip gets happy when Sheng cries, I conclude Sandip is a pretty lousy friend. Hahaha

Eric Escober - 6 years, 7 months ago

I think Sandip isn’t that much of a good friend either.

Diana Bradish - 1 year, 2 months ago

You can see the S of that Sandip, and Sheng is more like Meng.

Saya Suka - 3 months, 2 weeks ago

La respuesta puede hacerse simplemente descartando las opciones de respuesta. Las tres primeras se descartan porque tracy siempre estará triste y sheng nunca será feliz si ella no lo es.

Francisco Ramirez - 4 years, 6 months ago

I was actually gonna write all the days, but I noticed Tracy would never be happy and therefore neither would Sheng, and upon looking at the answers, only one option could be right.

José Fonseca - 2 years, 10 months ago

wow my mind is spinning in circles but good question!

Austin Li - 10 months, 1 week ago

Flewk Isdead
Aug 27, 2014

Sandip, Tracy, Jamal, and Sheng are best friends
Sandip enjoys watching Sheng cry, so Sandip is happy today only if Sheng was sad yesterday.

wtf.

I don’t think Sandip is a very good friend to Sheng either.

Diana Bradish - 1 year, 2 months ago

Richa Agrawal
Jul 11, 2014

Tracy is sad on day one, so she will always be sad, as her happiness depends only on herself. And since Tracy is never happy, Sheng can never be happy as well (AND relation with Tracy) Sheng is always sad, so sandip would always be happy and since sandip is happy, jamal is happy (OR relation with Sandip).

Member Wilcox
Jul 10, 2014

Tracy starts sad and never changes. Sheng can then never be happy either. Sandip is happy on the second day and ever after, because Sheng was always sad. That makes Jamal happy on the 3rd day and ever after. So they converge on a state where Tracy and Sheng are sad, while Sandip and Jamal are happy.

NOTE: This is a grim question and I don't understand why Sheng could be best friends with Sandip.

Completely agreed.

Annie W. - 6 years, 3 months ago

I definitely agree with you.

Diana Bradish - 1 year, 2 months ago

Annie W.
Feb 22, 2015

Just list their relative emotional states:

Day 1- Sandip-S, Tracy-S, Jamal-S, Sheng-S

Day 2-Sandip-H, Tracy-S, Jamal-S, Sheng-S

Day 3-Sandip-H, Tracy-S, Jamal-H, Sheng-S

This final state repeats itself FOR ETERNITY. Sandip is kind of a jerk.

Jerk = happy sadistic sob?

Saya Suka - 3 months, 1 week ago

Bassem Salem
Jan 15, 2015

Since Tracy is independent, and she started off sad. Then she will always be sad. Since Sheng is dependent on both Jamal and Tracy being happy. He will always be sad for Tracy. Since Sandip depends on Sheng being sad. He will start being happy on the second day and continues that way. Since Jamal depends on either Sandip or Sheng being happy. Then he will start being happy on the third day for Sandip and continues on.

so on the third day they will reach this state of stability

Brock Brown
Mar 8, 2015

Python:

sandip_y = False
sheng_y = False
jamal_y = False
tracy_y = False
while True:
    sandip = not sheng_y
    sheng = tracy_y and jamal_y
    jamal = sandip_y or sheng_y
    tracy = tracy_y
    if (sandip,sheng,jamal,tracy)==(sandip_y,sheng_y,jamal_y,tracy_y):
        break
    sandip_y,sheng_y,jamal_y,tracy_y = sandip,sheng,jamal,tracy
print "Sandip:", sandip
print "Sheng:", sheng
print "Jamal:", jamal
print "Tracy:", tracy

Nice solution! This code makes it easy for you to evaluate alternative arrangements.

Do you think all starting states will lead to the same endpoint or are there multiple repeating states? Also, I wonder if there are any sets of states that cycle between one another $\{S_1 \rightarrow S_2 \ldots \rightarrow S_n \rightarrow S_1\}$ ?

Josh Silverman Staff - 6 years, 3 months ago

Jerald Junio
Nov 21, 2014

Tracy will be sad forever because she would only become happy if she was happy yesterday which is not. Then Sheng would be happy if and only if Tracy is happy yesterday, which is not going to happen, so she will be forever sad as well. Sandip, who I assume is a sadist (kidding), will be become the first one to be happy because Sheng is sad on day 1, so Sandip will be happy the day after which is day 2. On day 3, Jamal will be happy because Sandip was happy yesterday.

Conclusion:

Tracy and Sheng: Forever Sadness

Sandip: Forever Happiness after day 1

Jamal: Forever Happiness after day 2

Faizal Ardian Putra
Jul 3, 2014

So look on the Tracy. It said that all of them are sad and. If Tracy were sad yesterday. So tomorrow she will sad. And sandip enjoys when sheng is sad. Sandip is enjoy. And Jamal is happy when one of sandip or sheng is happy or bother of them. Sandip happy = Jamal happy.sandip happy, sheng sad, Jamal happy, Tracy sad

Saya Suka
Feb 28, 2021

Living the OR life is the best. You take any happiness you can get however small it is and reflect + radiate those back for others around you.

STABLE STATES FOR THESE BFFS

Friend	Bad mood	Good mood
Tracy	Sad	Happy
Sheng	Sad	Happy
Sandip	Happy	Sad
Jamal	Happy	Happy

It's better if Sandip could influence Tracy with his happiness, even though that will come bite him back in return.

Saya Suka - 3 months, 2 weeks ago

Ahmed Obaiedallah
Jul 19, 2015

Tracey will always be sad so Sheng will always be sad

Sandip will become Happy the very next day as a result of Sheng sadness

And a day after Jamal will be happy due to Sandip happiness

and it'll remain as such

Mateus de Almeida
Jun 8, 2015

Tracy is independent, therefore she is always sad

Due to the fact that Tracy is always sad so will be Sheng

At the day after the first Jamal is sad because everyone was sad

Sandip is Happy on day 2 because Sheng was sad the day before.

On day 3 jamal gets happy because Sandip was hapoy the day before.

from day 3 onwards they enter a steady state because tracy will always be sad, which makes sheng always be sad, which makes sandip always happy, which makes jamal always happy

It's always happy at the banana stand

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