Math Is Fun Forum

juantheron

Member

Registered: 2011-10-19

Posts: 312

5 digit no

the no. of 5 digit no. that can be formed using the digit 0,1,2,3,4,5 that are divisable by 6 when repetition is not allowed is

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 5 digit no

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: 5 digit no

hi

i got  4*4*3*2*1+5*4*3*2*1=9*4*3*2=36*6=216

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 5 digit no

Hi;

I get 312:

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: 5 digit no

five digit numbers are at question here!

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 5 digit no

Yikes you are correct it is 5.

Then there are 108.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: 5 digit no

hi bobbym

i think you're missing a lot of numbers.e.g. i can't find 10245 anywhere.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 5 digit no

10245 is not divisible by 6.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: 5 digit no

oh,yeah.i forgot about that condition.

but i still think you should get the number of them numerically and not by trial and error.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 5 digit no

Computer is the fastest way and it is not trial and error. It only did it once. Also, as you should know
I always work backwards from the solution to the method.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: 5 digit no

i think that using computers to solve math problems is not good,unless you have to do something that requires a long time,like tasting the 198 algorithm.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 5 digit no

Have you read or seen any of Doron Zeilberger's work or his lectures?
He always uses a computer, so do gAr and I.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

TheDude

Member

Registered: 2007-10-23

Posts: 361

Re: 5 digit no

A number is divisible by 6 iff it is divisible by 2 and by 3.  This means that the numbers we want must end in 0, 2, or 4 and the sum of the digits
must be a multiple of 3.  Choosing 5 out of 6 numbers is equivalent to removing 1 out of 6 numbers, and the sum of the digits we are given is 15.
So, in order for the 5 digits we use to add up to a multiple of 3 we know that the one digit that is not used must be a multiple of 3, which in this
case is either 0 or 3.

Knowing all of that our calculations are pretty straightforward.  For numbers that end in 0 we must count all permutations of all four out of 1, 2, 4, 5,
which is 24.  So there are 24 legal numbers that end in 0.

For numbers that end in 2 we first count the number of permutations of all three of 1, 4, 5, which is 6.  For each permutation there are three
possible positions to place 0 and four possible positions to place 3, giving us a total of 6*3 + 6*4 = 42 legal numbers that end in 2.  This process
is identical for numbers ending in 4.  So our final answer is 24 + 42 + 42 = 108.

---

Wrap it in bacon