Re: Binary System Problem

• To: mathgroup at smc.vnet.net
• Subject: [mg18659] Re: [mg18621] Binary System Problem
• From: "Don Piele" <piele at cs.uwp.edu>
• Date: Thu, 15 Jul 1999 01:45:48 -0400
• References: <199907130501.BAA09602@smc.vnet.net.>
• Sender: owner-wri-mathgroup at wolfram.com

```Frieder,

Your problem is not well defined since you did not say how many zeros you
want
to include. There are an infinite number of binary numbers with a fixed
number of 1's.

Here is a solution that lets you decide how many zeros to allow.

insertZero[l_List] := Table[Insert[l, 0, {i}], {i, Length[l] + 1}]

numberOfZeros = 2;
listOfOnes={1,1,1,1};

Nest[Flatten[Map[insertZero, #], 1] & , {listOfOnes},  numberOfZeros] //
Union

{{0, 0, 1, 1, 1, 1}, {0, 1, 0, 1, 1, 1}, {0, 1, 1, 0, 1, 1}, {0, 1, 1, 1, 0,
1}, {0, 1, 1, 1, 1, 0}, {1, 0, 0, 1, 1, 1}, {1, 0, 1, 0, 1, 1}, {1, 0,
1,
1, 0, 1}, {1, 0, 1, 1, 1, 0}, {1, 1, 0, 0, 1, 1}, {1, 1, 0, 1, 0, 1},
{1,
1, 0, 1, 1, 0}, {1, 1, 1, 0, 0, 1}, {1, 1, 1, 0, 1, 0}, {1, 1, 1, 1, 0,
0}}

FromDigits[#, 10] & /@ %

{1111, 10111, 11011, 11101, 11110, 100111, 101011, 101101, 101110, 110011, \
110101, 110110, 111001, 111010, 111100}

Is this what you wanted?
D Piele

==================================================

----- Original Message -----
From: Frieder Schweigert <FSchweigert at airplus.de>
To: mathgroup at smc.vnet.net
Subject: [mg18659] [mg18621] Binary System Problem

> Hi,
>
> does anybody know an algorithm or generating system for
> those binary numbers with a fix amount of '1's,
> for example (four times '1'):
>
>  1111
> 10111
> 11011
> 11101
> 11110

```

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