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Guesstimation 2.0: Solving Today's Problems on the Back of a Napkin

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Simple and effective techniques for quickly estimating virtually anything

Guesstimation 2.0 reveals the simple and effective techniques needed to estimate virtually anything―quickly―and illustrates them using an eclectic array of problems. A stimulating follow-up to Guesstimation , this is the must-have book for anyone preparing for a job interview in technology or finance, where more and more leading businesses test applicants using estimation questions just like these.

The ability to guesstimate on your feet is an essential skill to have in today's world, whether you're trying to distinguish between a billion-dollar subsidy and a trillion-dollar stimulus, a megawatt wind turbine and a gigawatt nuclear plant, or parts-per-million and parts-per-billion contaminants. Lawrence Weinstein begins with a concise tutorial on how to solve these kinds of order of magnitude problems, and then invites readers to have a go themselves. The book features dozens of problems along with helpful hints and easy-to-understand solutions. It also includes appendixes containing useful formulas and more.

Guesstimation 2.0 shows how to estimate everything from how closely you can orbit a neutron star without being pulled apart by gravity, to the fuel used to transport your food from the farm to the store, to the total length of all toilet paper used in the United States. It also enables readers to answer, once and for all, the most asked environmental question of our paper or plastic?

384 pages, Paperback

First published April 1, 2008

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Lawrence Weinstein

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5 stars
114 (26%)
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139 (32%)
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129 (30%)
2 stars
36 (8%)
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Displaying 1 - 30 of 34 reviews
Profile Image for Terri.
376 reviews16 followers
February 1, 2011
I understand base ten, took algebra, calculus, and trig in high school (and got good grades at those), and have studied probability and statistics in college (at both the Bachelor's and Master's levels), so even though math isn't my strong suit, I am fairly competent at it. But I was confused by page 4 of this book - the authors present an equation and then the answer without the crosswalk between the two. Skimming ahead, I see that this book and I are not going to get along at all. One question requires an idea of how much food costs - the authors estimate it at somewhere more than 5% and less than 50% of a person's income and then pick a percent in between at random. That is how most of the answers in this book are figured. I find wildly random guesses like that completely useless. Even my husband, who does statistical analysis for a living was impatient with this book and couldn't get through it.
Profile Image for Joanna Chen.
9 reviews9 followers
August 27, 2010
Amazingly interesting set-ups for conquering estimations. Gives lots of useful figures that all people should know and teaches you how to quickly solve your own large scaled problems! Also great for interview questions.
Profile Image for Mender.
1,440 reviews13 followers
January 31, 2016
I'm actually not sure if I read this or a version that was 2.0 - but there's no 2.0 listed on the author's booklist, so we'll say it was this one. It presents guesstimated problem solving to really obscure and stupid questions and then solves them. There's no story tying anything together, it's like one of those quiz books where every page is just random stuff that caught the author's interest.

Which is actually really boring.

I flipped through, there weren't any problems I actually wanted to know the solutions to, so I didn't stick around to find out the method. If I ever feel like inventing problems for their own sake so I can pretend to solve them, rather than you know, actually solving a real problem... I might come back to it. Doubtful though.
Profile Image for Aathavan.
67 reviews7 followers
November 18, 2009
I thoroughly enjoyed this book. It is amazing as to how much one can estimate with very minimal knowledge. Some of the problems that stand out are

- what are the odds /mile of dying in a plane and in a car?
- How much star debris would a supernova dump on earth?
- how much more corn fields would we need to convert to ethanol based fuel economy?
- What is the power density of the sun?



422 reviews21 followers
June 15, 2018
I like the idea of this book: a collection of practical math problems that can be solved in 5 mins. Though the book starts very well, it grows repetitive quite fast. In most problems, the key factor is to guess correctly the value ranges of entities, and it's very hard to do with many Americancentric questions.
Profile Image for Alb85.
352 reviews11 followers
December 11, 2024
Libro che aiuta a risolvere i problemi di Fermi, cioè spiega come fare stime nel caso di informazioni parziali.

Non mi fa impazzire la struttura del libro.
La prima metà contiene gli esercizi da risolvere in forma di domande, con immagini e suggerimenti. Solo all'inizio di alcuni capitoli ci sono delle nozioni teoriche.
Nella seconda metà, quella realmente interessante, ci sono di nuovo gli esercizi da risolvere e, cosa importante, le soluzioni.

Questi i principali suggerimenti espliciti che si trovano nel libro:
- usare la notazione scientifica
- quando nel risolvere un problema si considerano sia numeri molto piccoli che molto grandi, si deve ragionare su scala logaritmica. Significa che se abbiamo un valore che secondo noi è compreso tra un range, ad esempio tra 10 e 1000, dobbiamo fare la media geometrica, cioè si fa la media degli esponenti. In questo caso (1+3)/2=2 quindi 100.
- Arrotondare senza farsi troppi problemi nel considerare solo un decimale dopo la virgola.
- Usare sempre le seguenti unità per fare i calcoli: metri, secondi, kg, per poi convertirle in base al coefficiente della notazione scientifica, in modo che il valore abbia una o due cifre.

La maggior parte dei suggerimenti interessanti però si devono cercare nelle soluzioni. Ne menziono alcuni:
- per stimare la distanza, basta partire dalla velocità di un mezzo che la percorre e il tempo che impiega. Ad esempio, per stimare la lunghezza dell’Italia. I treni da Milano a Reggio Calabria impiegano circa 10 ore, a velocità media di 100 km/h quindi l’Italia è lunga circa 1000 km.
- per stimare il tempo per riempire di acqua qualcosa: il rubinetto di casa riempie una bottiglia da litro in circa 5 secondi, la portata è 0.2 L/sec. Quindi: tempo richiesto = volume della cosa da riempire / portata.
- Quanto pesa x? stima volume e densità: x galleggia? allora la densità è quasi come quella dell'acqua 1 t/m^3 (o 1 kg/L). Non galleggia ma è meno densa del ferro (cha ha densità 10 t/m^3)? allora fai la media geometrica tra densità acqua e ferro. In fine: peso = densità * volume.
- La percentuale di tempo una persona media dedica a una certa attività è uguale alla percentuale di persone in un momento che fanno quell'attività. Ad esempio, se in media passi il 10% del tuo tempo in volo allora in qualsiasi momento sarà in volo in 10% della popolazione.
- il volume o area di x (essere umano, animane, pianeta) si può approssimare a un parallelepipedo rettangolo (come una scatola) o più semplicemente a un cubo. Si sbaglia solo di qualche fattore minore di 10.
- g si può stimare a 10 m/s^2.

In sintesi, molti contenuti interessanti, sulla forma lasciamo perdere.
Profile Image for Paulo.
Author 2 books7 followers
August 23, 2023
A premisa de partida é moi interesante: son os coñecidos coma problemas de Fermi, basicamente problemas mediante un cálculo rápido (con poucas variables e operacións) de cantidades que semellan a simple vista imposibles de estimar.

Así que de inicio o libro resulta atraente, e os primeiros apartados conseguiron terme facendo mentalmente os meus propios cálculos para comparalos cos dos autores. Pero rapidamente caín na desidia, xa que enseguida se volve moi repetitivo, hai pouca variedade e fai o mesmo tipo de cálculos unha e outra vez. Quizais é que os exemplos non están ben escollidos, ou quizais é que o tema non daba para tanta extensión e en formato de libro faise demasiado.

No tocante aos cálculos en si, tamén houbo algunhas cousas que non me gustaron. A primeira é o americanocentrismo (incluso aínda que un dos autores é británico! Como é iso posible?), tanto que fai complicado seguir algúns dos razoamentos para alguén que non viva nos EUA. A ver, oh, non hai medidas que sirvan de comparación que poidan ser un pouco máis internacionais?

Por outro lado, en demasiadas ocasións a validez da estimación recae simplemente en acertar co rango de valores a tomar nunha única variable. Demasiado simplista. Ademais, non me gusta nada como para un rango ás veces toman como valor para facer os seus cálculos a media xeométrica, outras veces a media aritmética e en ocasións un que non é nin unha nin outra, e fano de forma aparentemente aleatoria. Semella demasiada "cociña" para que saian os valores que queren.

Por último, tamén me parece case aleatorio como unhas veces piden que non se busque cal é o valor real de algunha variable e prefiren poñerse a estimalo, pero noutros apartados si toman ese valor real para outras variables, sen mediar explicación de por que uns si e outros non.
Profile Image for Harry Harman.
833 reviews17 followers
December 26, 2021
These problems are frequently called “Fermi problems,” after the legendary physicist Enrico Fermi. During one of the first atomic bombtests, Fermi supposedly dropped a few scraps of paper as the shock wave passed and estimated the strength of the blast from the motion of the scraps as they fell.

To take the approximate geometric mean of any two numbers, just average their coefficients and average their exponents.* In the clown case, the geometric mean of one (100)† and 100 (102) is 10 (101). The exponent is the power of ten and the coefficient is the number (between 1 and 9.99) that multiplies the power of ten.

a tall building (100m or 300ft), a small mountain(1000m), Mt Everest(10,000m),the height of the atmosphere (105 m), the distance from New York to Chicago (106m), the diameter of the Earth (107 m), or the distance to the moon(4×108 m

When we multiply numbers, we multiply coefficients and add exponents.

the silliness of having too many digits is illustrated by the following anecdote. Suppose that you ask a museum guard how old a dinosaur skeleton is. He responds that it is 75million and 3 (75,000,003) years old. When you look puzzled, he explains that when he started the job three years ago, the skeleton was already 75million years old.

all the people on Earth would f it in a square that is 30km or 20mi on a side. That’s the area of a large city such as Los Angeles. Now let’s give every family a house and a yard. 1 × 10^6 mi^2 (one million square miles). While it sounds like a lot, it is only the area of Alaska. That is only 1% of the surface area of the Earth.
Profile Image for Sandeep Guguloth.
77 reviews4 followers
October 3, 2022
Once you accept the basic premise of the book, i.e., "we're gonna try and guess the order of magnitude of the quantities or values we're interested in, and not the actual numbers", you can appreciate the methods used. The book is self-aware of the limitations of the methods used, and acknowledges the differences between the guesstimated values and actual real-world quantities. It has a good range of interesting problems across various subjects of interest. Will be useful to those who are preparing for the semi-technical parts of engineering job-interviews.

An interesting way to read this book, is to try and solve the problems yourself, before you read through the method used in the book; and then compare the final estimates.
Profile Image for Viljami Kuosmanen.
18 reviews9 followers
January 22, 2019
Mildly amusing examples of problems that can be solved with back-of-napkin maths.

Perhaps a nice exercise book for someone looking to hone in on their estimation skills.

I just didn’t get much out of it to be honest. Every problem I read (admittedly skipped quite a few boring ones), the solutions were obvious and not very imaginative. Many required the usage of a calculator, which was disappointing.

I learned that a geometric mean of lower and upper bounds is often a good starting point for estimates. Also that a gerbil’s power output is greater than the Sun (by mass).

2/5
Profile Image for Jessada Karnjana.
584 reviews8 followers
April 17, 2022
ค่อนไปทางขำ ๆ อ่านแล้วยิ้มได้ ... "เกสติเมชั่น" ว่าด้วยการเดาอย่างมีชั้นเชิง เป็นการคำนวณง่าย ๆ เพื่อประมาณสิ่งที่เราอยากรู้ เช่น ปีที่ผ่านมาชาวอเมริกันกินแตงกวาดองถ้านำมาต่อกันยาวเท่าใด (เฉลย ไกลกว่าระยะห่างระหว่างโลกกับดวงจันทร์), ตอนนี้มีคนแคะจมูกอยู่กี่คน (เฉลย 10 ล้านคน), บุหรี่ 1 มวนบั่นทอนชีวิตกี่นาที (เฉลย 5 นาที แต่จากข้อมูล BMJ 11 นาที), ถ้าเปิดก๊อกน้ำใส่ให้เต็มมหาวิหารเซ็นต์ปอลใช้เวลานานเท่าไร ...
Profile Image for David Hilbish.
14 reviews2 followers
November 21, 2024
Repetive. It was simply lots of samples and would not teach someone who does not kn ow how to estiamte the process.
2 reviews
January 10, 2018
This is a light-hearted and enjoyable book. Only very basic maths required, and not too much knowledge is assumed (though common sense and general knowledge do help). Useful as this kind of question occurs in interviews, and it is a useful still to have anyway.
75 reviews
March 12, 2017
Guesstimating is the ability to think abstractly and come up with a logical answer. How many golf balls in a school bus? How many diapers in a day in China? How big was that explosion? How far does the earth travel in a year? The one thing I remember from this is the number of seconds in a year is pi x 10 to the 7th. Not sure how that is handy, but it is pretty cool. The book focuses on a series of problems and then gives the solution with what should be (crappy educational system aside) common sense, well known constants and a bit of basic math. I'll admit I was stumped by a few, but mostly in the electrical amp/volt/ohm neck of the woods.
Profile Image for Maurizio Codogno.
Author 66 books143 followers
November 15, 2010
[se vuoi una mia recensione più seria di questo libro, va' su Galileo, "http://www.galileonet.it/recensioni/1..." !]
La spannometria è la regina delle scienze approssimate, come scrissi a suo tempo sul mio Gergo Telematico (http://xmau.com/gergo/ ). Un po' più seriamente, quella di stimare i risultati a partire da dati apparentemente incompleti è un'arte che ha anche dei risvolti pratici, visto che permette di verificare con carta e penna se i numeri che si ottengono sono coerenti con quelli che sono stati indicati. In questo libro abbiamo così un gran numero di "Problemi di Fermi", chiamati così negli States perché il grande fisico amava porli ai suoi collaboratori. Le domande sembrano assurde, spaziando da "quanti accordatori di pianoforte ci sono a Roma?" a "quant'è l'equivalente energetico in lattine di Coca-Cola della benzina consumata da tutti gli autoveicoli in Italia?". Ma quello che conta sono altre cose: imparare a suddividere il problema in passi gestibili, sapere quali sono gli arrotondamenti fattibili, e anche mettere in pratica le formule fisiche (Weinstein è un fisico e tiene un corso universitario proprio su questi temi, mentre Adam è matematico). Il testo è scritto in maniera umoristica, o per meglio dire fredduristica; siete avvisati. Ultima nota di merito per la traduttrice Luisa Doplicher e per la "rilettrice" Marinella Lombardi, che hanno fatto un bel lavoro nell'italianizzare i riferimenti. Non c'è nessuna differenza tecnica nel valutare il numero di chilometri percorsi dagli italiani o il numero di miglia percorse dagli americani; ma per un lettore nostrano la prima stima è molto più interessante.
7 reviews
February 9, 2010
This book is meant to be read fast, the reader dwelling on physics formulas and arithmetic only in intriguing areas. It is a book of big numbers; you understand logarithms inadvertently by its end. The book covered high-school physics well; it contains "word problems" about size, speed, astronomy, electricity, pressure--all the fun stuff. Lots of conversions to standard metric units. Handy technique for quickly estimating using the mean of exponents. Examples of problems: What percentage of U.S. land mass would need to be covered with solar panels to supply our current power needs? and How many people in the world are currently brushing their teeth? Sometimes silly questions, but there is always the underlying point that we are a lot of people and our small actions add up hugely.
Be warned that the book is rife with corny humor that occasionally evokes chortles.
Profile Image for Anya.
385 reviews
September 21, 2013
I'll admit it, this was a really difficult read for me. Studying abstract math and only thinking about logic for years has only been detrimental to my ability to think about applied problem solving. This is a really short book, but each section left me thinking for hours afterward, trying to figure out distances and volumes, wanting to measure items and calculate things. Basically, it left me thinking about all the things I tried to avoid in math and physics courses for my whole life: the real world.
5 reviews
March 23, 2012
A physics professor at my school is one of the authors of this book. We are using it as the text for a seminar he teaches called Physics on the back of an envelope. It is a lot of fun and really helps me learn to think through things with quick estimates and comparisons. The book itself is a quick, easy read with lots of examples and hints. After a bit of practice it is fun to come up with my own questions to estimate.
Profile Image for Isaac.
42 reviews
September 8, 2013
A good introduction to estimations or so-called "Fermi problems". Lots of fun estimates to have a go at. Mostly only arithmetic is required though some problems require a knowledge of volume calculations and basic concepts from physics. Good source of questions for teachers wanting problem solving material without excessive discipline content required to actually do the problems.
Profile Image for Alexander Ray.
13 reviews2 followers
March 27, 2016
The introductory part of this book contains a good overview on Fermi estimation, and particularly why and how to use Approximate Geometric Means.

I would recommend checking out the book (from the library) just to read the short introduction, and flip through a couple of the problems to see what they're like.

You can 80/20 this book with about 10 minutes.
136 reviews2 followers
January 3, 2014
The first half was great and it was fun to work out estimates, but towards the end it got ridiculously convoluted and technical (coming from someone with a generally alright knwlledge of maths and science).
Profile Image for loonchies.
239 reviews26 followers
January 8, 2018
There are not only some brilliant questions which are interesting to solve, but also many nonsense questions ( or maybe I just couldn't understand them)
In the beginning it was interesting, it didn't attract me at all, even I love mathematics.
Profile Image for Teo.
9 reviews
January 4, 2009
wow, learnt that almost 10million people are digging their nose at every instant
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