which is the smallest even number...

[enzocreti]

which is the smallest even number N (in base 10) such that converted in base 2 contains five 1's?


I guess 94?

[Uncwilly]

62₁₀ is 111110₂

[retina]

N = 2

2₁₀ = 1.1111.....₂

[VBCurtis]

Originally Posted by retina

N = 2

2₁₀ = 1.1111.....₂

That contains more than 5 ones.

[retina]

Originally Posted by VBCurtis

That contains more than 5 ones.

Yes. The criterion is that is contains five ones. And it does. It also contains some more ones. It didn't say five ones and only five ones.

[VBCurtis]

It also didn't say "at least 5 ones".

If I asked for a recipe using 3 eggs, and you gave me a recipe using infinite eggs, I wouldn't find you very helpful.

[retina]

Originally Posted by VBCurtis

If I asked for a recipe using 3 eggs, and you gave me a recipe using infinite eggs, I wouldn't find you very helpful.

But you might find me pedantic.

[M344587487]

If we're going for pedantry points then you missed negative numbers. Pick a representation of negative numbers in binary, pick a fixed or variable word representation, pick how you define smallest. Naturally you'd think a<b for smallest, but the base 10 specification allows for an interpretation as the least number of digits when written in base 10.

-0 is 11111 in one's complement with a 5 bit word. It's the default winner of "least number of digits when written in base 10".

[retina]

Originally Posted by M344587487

-0 is 11111 in one's complement with a 5 bit word. It's the default winner of "least number of digits when written in base 10".

2 and -0 have the same "number of digits when written in base 10". But 2 has fewer characters than -0.

But a true pedant might interpret "smallest" to be numerical value. And if we are allowed to twist the definition boolean arithmetic with infinity: "-(∞ AND (∞ XOR 1))" has an infinity of 1's with the last digit as 0.

Now we just need to define AND and XOR when dealing with infinities.

[xilman]

Originally Posted by VBCurtis

It also didn't say "at least 5 ones".

If I asked for a recipe using 3 eggs, and you gave me a recipe using infinite eggs, I wouldn't find you very helpful.

Reminds me of the programmer who, before he went shopping, was told by his wife: "Buy a loaf of bread and, if they have any eggs, get a dozen." He came back with 12 loaves of bread and no eggs.

[Dr Sardonicus]

Originally Posted by retina

N = 2

2₁₀ = 1.1111.....₂

The question specified "converted in base 2."

Please explain the algorithm by which you convert 2₁₀ into base two, so as to get 1.111... rather than 10.