Problem-solving: explaining cause and effect

B2
60 min
Premium
1

Think about these questions before watching. Share your ideas with a partner.

  1. Describe a time when a seemingly small mistake led to a much bigger, more complicated problem. What was the initial cause and what were the ultimate consequences?
  2. When you're faced with a complex problem under intense pressure, what is your typical approach? Do you tend to act immediately or do you prefer to take a moment to think systematically?
  3. In what ways has technology made us better at problem-solving, and in what ways might it have made us less resourceful when our tools fail?
2

Watch the video carefully. Pay attention to the main ideas and key details.

Video script88 segments · click a timestamp to jump

After years of experiments,

you’ve finally created the pets of the future–

nano-rabbits!

They’re tiny, they’re fuzzy…

and they multiply faster than the eye can see.

In your lab there are 36 habitat cells,

arranged in an inverted pyramid,

with 8 cells in the top row.

The first has one rabbit,

the second has two, and so on,

with eight rabbits in the last one.

The other rows of cells are empty…

for now.

The rabbits are hermaphroditic,

and each rabbit in a given cell will breed once

with every rabbit in the horizontally adjacent cells,

producing exactly one offspring each time.

The newborn rabbits will drop into the cell

directly below the two cells of its parents,

and within minutes will mature and reproduce in turn.

Each cell can hold 10^80 nano-rabbits –

that’s a 1 followed by 80 zeros –

before they break free and overrun the world.

Your calculations have given you a 46-digit number

for the count of rabbits in the bottom cell–

plenty of room to spare.

But just as you pull the lever to start the experiment,

your assistant runs in with terrible news.

A rival lab has sabotaged your code

so that all the zeros at the end of your results got cut off.

That means you don’t actually know

if the bottom cell will be able to hold all the rabbits –

and the reproduction is already underway!

To make matters worse,

your devices and calculators are all malfunctioning,

so you only have a few minutes to work it out by hand.

How many trailing zeros should there be

at the end of the count of rabbits in the bottom habitat?

And do you need to pull the emergency shut-down lever?

Pause the video now if you want to figure it out for yourself.

Answer in 3

Answer in 2

Answer in 1

There isn’t enough time to calculate the exact number of rabbits in the final cell.

The good news is we don’t need to.

All we need to figure out

is how many trailing zeros it has.

But how can we know how many trailing zeros a number has

without calculating the number itself?

What we do know is that we arrive at the number of rabbits in the bottom cell

through a process of multiplication –

literally.

The number of rabbits in each cell

is the product of the number of rabbits in each of the two cells above it.

And there are only two ways

to get numbers with trailing zeros through multiplication:

either multiplying a number ending in 5 by any even number,

or by multiplying numbers that have trailing zeroes themselves.

Let’s calculate the number of rabbits in the second row

and see what patterns emerge.

Two of the numbers have trailing zeros –

20 rabbits in the fourth cell and 30 in the fifth cell.

But there are no numbers ending in 5.

And since the only way to get a number ending in 5 through multiplication

is by starting with a number ending in 5,

there won’t be any more down the line either.

That means we only need to worry

about the numbers that have trailing zeros themselves.

And a neat trick to figure out the amount of trailing zeros in a product

is to count and add the trailing zeros in each of the factors –

for example, 10 x 100 = 1,000.

So let’s take the numbers in the fourth and fifth cells

and multiply down from there.

20 and 30 each have one zero,

so the product of both cells will have two trailing zeros,

while the product of either cell and an adjacent non-zero-ending cell

will have only one.

When we continue all the way down,

we end up with 35 zeros in the bottom cell.

And if you’re not too stressed about the potential nano-rabbit apocalypse,

you might notice that counting the zeros this way

forms part of Pascal’s triangle.

Adding those 35 zeros to the 46 digit number we had before

yields an 81 digit number –

too big for the habitat to contain!

You rush over and pull the emergency switch

just as the seventh generation of rabbits was about to mature –

hare-raisingly close to disaster.

3

Answer these questions in your own words. Support your answers with evidence from the video.

01What was the specific technical problem that created the emergency, and what caused it?
Sample answerThe main problem was that all the trailing zeros from the final rabbit count were missing. This happened because a rival lab had sabotaged the scientist's computer code, which meant the true size of the number was unknown.
02In what way do the nano-rabbits reproduce to populate the lower cells of the habitat?
Sample answerThe number of rabbits in a lower cell is the product of the rabbit populations in the two cells directly above it. Each rabbit in one cell breeds with every rabbit in the adjacent cell, and their offspring fall into the cell below.
03Why was the scientist able to ignore the possibility of new trailing zeros being created by numbers ending in 5?
Sample answerBecause after calculating the numbers for the second row, none of them ended in a 5. To create a new number ending in 5 through multiplication, one of the original numbers must end in 5. Since that possibility was gone after the first step, it wasn't a factor anymore.
04How did the final count of 35 trailing zeros help the scientist determine that the habitat was too small?
Sample answerThe scientist already knew the final number started with 46 digits. Adding 35 zeros to the end of that number resulted in a total of 81 digits. The habitat's maximum capacity was 10 to the power of 80, which is also an 81-digit number, but the calculated result was clearly larger, proving it would be a disaster.
4

Vocabulary for problem-solving

Vocabulary
These expressions will help you explain cause and effect more clearly when discussing problems and solutions.
Examples
to get out of hand — to become difficult or impossible to control
This idiom is often used to describe a situation that escalates and becomes chaotic. For example, 'The experiment started well, but the rabbit population quickly got out of hand.'
a chain reaction — a series of events where each one is caused by the previous one
This phrase can be used in scientific contexts, as in the video, or to describe social or economic events. For example, 'The initial error set off a chain reaction of system failures.'
to account for something — to consider or include a particular factor when making a calculation or plan
This is a semi-formal phrasal verb. You might say, 'The scientist forgot to account for the possibility of sabotage in her calculations.'
unforeseen consequences — results or effects of an action that were not expected or predicted
A useful phrase for discussing planning and risk. For example, 'Modifying the code had unforeseen consequences for the entire experiment.'
to work against the clock — to work very quickly because you have a limited amount of time
This idiom emphasizes urgency and pressure. For instance, 'With the system about to fail, the team had to work against the clock to find a solution.'
5

Decide if each statement is true or false. Correct the false ones.

01Each habitat cell was designed to hold a maximum of 10^80 nano-rabbits.
02The key to solving the problem quickly was to focus on adding the trailing zeros of the factors in the multiplication process.
03The experiment began with an equal number of rabbits in each of the eight cells in the top row.
04The scientist's calculations were sabotaged by a rival who added extra zeros to the final number.
05The scientist had to perform the calculation by hand because their equipment was malfunctioning before the experiment began.
6

Discuss these questions with a partner. Try to use vocabulary from the lesson.

  1. The video shows a scientific experiment that could easily get out of hand. Who should be responsible for preventing unforeseen consequences in scientific research—the individual scientists, their employers, or the government? At what point does scientific curiosity become too risky?
  2. Think about a major project or policy in your country. Can you describe how a failure to account for one small detail caused a chain reaction of problems for the public or the environment?
  3. In the video, the scientists had to work against the clock when their technology failed. In your own profession or studies, how would your team cope if your primary digital tools suddenly stopped working? What problems would arise and how resourceful do you think people would be?