# Puzzle – can you tell me a five digit number such that its first digit gives the number of zeroes in it. second digit the number of ones and so on to fifth digit showing number of fours in it?

1

• Qba
2015-09-11T15:15:14+05:30

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Actually we need to consider the fact that any number we put at the first place will have to be noted later in the number as the consecutive digits show how many repetitions of a specified digit we have in the whole number.

For example, if you write 3 in the first position:

3 _ _ _ _

You will have to write 1 in the fourth position because it specifies the number of 3 in the whole number, like this:

3 _ _ 1 _

Does it work though? Because then, we have a 1 and we have to state it in the number but if you we do that and write:

3 1 _ 1 _

the number of 1 will change. We can have one 1 only if it's in the second position, like this:

_ 1 _ _ _

-------

When we take all those data into consideration we can start thinking about the number we need here. I was able to find only one:

2 1 2 0 0

Let's check it:

2 times 0 ::       2 1 2 0 0         ✔
1 time 1 ::         2 1 2 0 0         ✔
2 times 2 ::       2 1 2 0 0         ✔
0 times 3 ::       2 1 2 0 0         ✔
0 times 4 ::       2 1 2 0 0         ✔

I hope that it helps :)