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The solution is correct, but I'd do it like this:

Seems about right.

Yeah, seems about right.

Bob wrote:

No.

Suppose n was the number. Let's say its decimal form is 0.00000...x...... Let x be the first non zero digit. There must be such a digit or else the number is zero. And say the next digits are y and z.

ie. n = 0.00000...xyz...... where every digit before x is zero. Change x to zero too. New number is 0.00000.....0yz....... so it's smaller. So the number we thought we'd found isn't the smallest.

Bob

Sure, this does work if the number is non-terminating, but what about a situation like this:

Let's suppose n is in the form x × 10^-p, where x and p are counting numbers. For example, let's suppose n = 125 × 10^-6 = 0.000125.

Let's make a sequence S where S₁ = n, and S_{z+1} is S_z but with the first non-zero digit replaced with 0.

Then, the sequence will go like this:

```
S_1 = 0.000125
S_2 = 0.000025
S_3 = 0.000005
S_4 = 0.000000 (not positive)
```

So we can see that this doesn't work all the time.

Let's make another sequence T, where T₁ = n, and T_{z+1} is T_z / 2. Here's how it goes now:

```
T_1 = 0.000 125
T_2 = 0.000 0625
T_3 = 0.000 03125
T_4 = 0.000 015625
...
```

Let's try it with a non-terminating number:

```
T_1 = 0.000 333333...
T_2 = 0.000 166666...
T_3 = 0.000 083333...
T_4 = 0.000 041666...
...
```

So halving *does* work all the time.

Sorry for the mistake, I fixed it.

KerimF, use the hide tag if you don't want to straight-up reveal the answer.

Remember: you can use the **hide** tag to make your answer hidden in a button.

Hi Jai,

As you say, Irene.

To not get italicized text, use the \text{} tag.

`area \ of \ a \ circle = \pi{r^2}`

gives

but

`\text{area of a circle} = \pi{r^2}`

gives

Wait, wouldn't it be "Find **that** number"?

Hello, MathAppreciator,

**Welcome to the forum **

If it was italic, sin(x) would really mean s×i×n×x.

Hi Opichem,

Welcome to the MIF forum!

The study of big numbers is also called "googology".

There are already dozens of variations of Wordle. One of them is Nerdle, which is based on math.

It is also possible to accommodate an infinite amount of infinitely many guests, like if you had infinitely many buses with infinitely many guests in each:

```
**|01 02 03 04 05 ...
--+------------------
01|01 02 06 07 15 ...
02|03 05 08 14 16 ...
03|04 09 13 17 25 ...
04|10 12 18 24 30 ...
05|11 19 23 31 39 ...
..|.. .. .. .. .. ...
```

Hello, can anyone tell me how to put a message inside a button?