A Classic Puzzle

Since they double themselves every minute, if the jar is full on 60th minute, it must have been half full on 59th minute. In the last minute, each bacteria doubles itself to fill the jar completely.

Mathematically, the amount of bacteria at any point would be

$2^{n}$

where n is the time elapsed in minutes. Therefore, after 60 minutes the jar would contain

$2^{60}$

particles of bacteria. If the jar is full after 60 minutes, then the amount of bacteria when it is half full would be equal to

$\frac{2^{60}}{2}$

Which, using the rules of exponents would be equal to

$2^{60 - 1}$ = $2^{59}$

and hence the answer is 59

If we want to use some notation for this, the function $n: \mathbb{N} \rightarrow \mathbb{N}$ that gives us the number of bacteria in the jar is given by

$n(t) = 2^{t+1}$

Where $t$ is the time in minutes. At $t = 60$ the jar is full and we have therefore $2^{61}$ bacteria in it. Let's say that at $t_{0}$ it was half-full, i.e.,

$n(t_{0}) = \frac{n(60)}{2} = 2^{60} = 2^{t_{0} + 1} \qquad \therefore t_{0} = 59$

it doubles in every minutes.

so, it was full in 60 minutes.and it was half in (60- 1) minutes=59 minutes.

This problem should be changed to "she observed the jar became full at exactly an hour". Since the jar was observed to be full, one cannot assume that it wasn't full at an earlier time, but stopped doubling because it was full. The correct answer would be one minute before the exact moment it became full.

Since they double themselves every minute, if the jar is full on 60th minute, it must have been half full on 59th minute and then each bacteria doubled itself to fill the jar completely. So, the correct answer is 59 minutes.

Let call the amount of bacteria to fill the jar $x$ .So we have:

$2^{60}=x,2^n=\frac{x}{2} \implies n=\frac{2^{60}}{2}=2^{60-1}=\boxed{\large{2^{59}}}$

Double on minute

60 have passed and full jar

-1 min makes half jar

This question is meant to trick the reader, as logically we want to say 30 minutes. The answer, however, is 59 minutes.

Solution: 2^60=full so, to halve the value we do 2^(60)/2 and find that 2^(59) is the final answer.

haha this kinda seems more like a trick question than a math question!

The jar is full of bacteria after an hour and the bacteria is doubling every one minute. So the jar is half of bacteria one minute before (59 minutes)

As the bacteria doubles in a minute it is only possible if the jar is half filled in the 59th minute

Exactly the same as my question hahah. Just logical thinking . the amount of bacteria of FIRST minute would be half of SECOND minute. SO.....when 60 minute as SECOND minute..the first minute would be 59minute

on 60th minute, it was full..so, 1 min before, it was half..thats why 1 min later it doubled to become full

since it is an classic example of exponential growth. So 22^60=full jar formula for exponential growth is ab^t=Growth a=initial value, b=growth rate 22^60/2=22^t therefore, t=59

The jar is full in 60 minutes with the bacterias having the quality of each doubling itself in 1 minute. It is half full in 2^60 / 2 = 2^60 / 2^1 = 2^59 which gives us the the answer as 59 minutes and it is correct!!!!!!!!!!!!!!

A each minute the bacteria doubles.. At 59min it will be half the jar then only it can be filled full jar at 60min

The bacteria doubles each MINUTE. This means that if it became full, then in the previous minute it was half-full. Also, I LOVE THE PROFESSOR LAYTON GAMES!!!

In the problem, it is written that the number of bacteria doubles each minute. Say for example, in the first minute, there are 2 bacteria, therefore at the 59th minute, the number of bacteria would be 5.76460752 x 10^17. And the next minute, it would multiply and therefore become 1.1529215 x 10^18, the double.