Odd Looks

In a four-digit number, $(a,bcd)$ we have 5 choices for $a$ because it can only be a 1, a 3, a 5, a 7, or a 9. There are also only 5 choices for each of $b$ , $c$ , and $d$ . This means that there are $5\cdot5\cdot5\cdot5=\boxed{625}$ so-called "odd looking" numbers.

There are five distinct odd digits (i.e. 1,3,5,7,9) that can go in the unit's place. Since repetition is allowed, there are still five distinct digits (i.e. 1,3,5,7,9) that can still go in the ten's place, the hundred's place and also in the thousand's place. By the multiplication principle, there are 5x5x5x5 = 625 different possibilities.

For those who think in code, here's a Python programme:

import math

Counter = 0

for x in xrange(1000, 10000):
    a = x % 10
    b = math.floor(x/10) % 10
    c = math.floor(x/100) % 10
    d = math.floor(x/1000) % 10

    if a % 2 == 1:
        if b %2 == 1:
            if c % 2 == 1:
                if d % 2 == 1:
                    Counter = Counter + 1

print Counter

The programme confirms that 625 is the answer by printing this value as the output.

If anybody has any ideas on how to improve my code, please share it with me.

Please consider: N = Number of options = (1, 3, 5, 7, 9) is 5 and d= Number of Digits in the Odd Looking Number = 4

Therefore , total number of Odd Looking numbers are N raise to power of d. = 5 x 5 x 5 x 5 = 625

There are $4$ digit places where we can put one odd number in each of them. From $1$ to $9$ , there are $5$ odd numbers ( $1, 3, 5, 7, 9$ ). All we need to do here is multiply across.

$5 \times 5 \times 5 \times 5 = \boxed{625}$

first place can be filled by 1, 3, 5, 7, 9 = 5

similarly, second, third, fourth places can be filled

therefore total numbers = 5 5 5*5 = 625

For each digit we have $5$ choices $(1, 3 ,5,7~~ \text{and}~~ 9)$ As the number has $4$ digits have $5 ^ 4$ choices and so we have $5 ^ 4 = 625$ "odd-looking" numbers.

odd number are 5 (1,3,5,7,9)

4 digits x x x

5x5x5x5=625

There are 5 single-digit odd numbers. 5 times 5 times 5 times 5, or 5^4, gets you your answer- 625.

The set of odd single digits: {1,3,5,7,9}.

The set odd looking four digit numbers: {1111, 1113, ............, 9999}.

Four odd digits chosen from five possible digits: $5*5*5*5$ = 5^4 = 625.

Before I begin, let me apologise profusely for how badly I manage to explain myself, as my thought process is quite distorted from the norm, some would say. Again, sorry :)

First set of odd looking integers above 1000: 1111, 1113, 1115, 1117, 1119. This makes 5 total integers. From there, it's obvious that there will be 5 sets of those for every other hundred integers. (e.g. 1100, 1300, 1500, etc.) as we would exclude 1200, 1400, etc.

This leaves us with 5*5 [for the individual sets of ten] *5 [accounting for the 5 odd hundreds....] = 125 odd looking integers for 1111 through 1999.

Multiply this 125 by 5 once again (for the remaining 5 thousand-sets of odd looking integers) and you have 625, the final answer. This is because the answer for how many odd looking numbers from 1111 through 1999 is the same for 3111 through 3999, 5111 through 5999, and etc.

Sorry again for the distorted thought train :P

4-digit odd looking numbers is \overline{abcd}. The odd numbers is 1 3 5 7 9. Number a of \overline{abcd} have 5 case. Number b of \overline{abcd} have 5 case. Number c of \overline{abcd} have 5 case. Number d of \overline{abcd} have 5 case. So, there are 5 x5x5x5 = 625 the 4-digit odd looking numbers

all the places can be filled by 1, 3, 5, 7,9 that is 5 ways therefore total number of ways = 5 5 5*5 = 625 (as repetition is allowed)

5^4=625

1,3,5,7,9 are odd. 5 numbers 4 positions. 5x5x5x5=Ans

We have 5 odd numbers (1,3,5,7,9) 5 C 1 X 5 C 1 X 5 C 1 X 5 C 1 = 625

Let be A B C D is a four digit number with all digits odd. We have 1,3,5,7 and 9 as odd and it totals 5, so chances of getting an odd at A = 5, same at B,C and D. so total probability comes out 5 X 5 X 5 X 5 = 5^4 = 625 (there are 625 four digit odd looking numbers in our modern day maths).

by the general principle of counting as there are four places the answer should be 5^4=625 as there are five odd numbers={1,3,5,7,9}

odd digits 1,3,5,7,9 in these 4 digit numbers any digit can be filled with any of odd digits then no of odd numbers are 5 5 5 5 5=625

set of odd digits={1 ,3,5,7,9} Number of ways of writing 4 digit odd looking=5.5.5.5=625

You have 4 spaces or 4 digits. The number of single digit odd numbers is 5, numbers 1,3,5,7 and 9 respectively. it did not state whether the numbers may not be repeated so therefore you have 5 choices of odd number per slot. the numbers of slots will serve as exponent therefore 5^4 = 625 or per slot you insert the number five and you will have 5x5x5x5 = 625

This solution is based on logic. I did not use any formula.

since, the odd digits are 1,3,5,7,9. So, total four digit number that can be forms using these digits are 5^4 = 625 (remember, repetition is allowed.)

every digit of a four digit number can have any one of 5 odd numbers. Therefore all the four digits simultaneosly can have 5^4 combinations = 625 ways

by using filling slots. 5x5x5x5 = 625.

from 0-10 there are 5 odd numbers namely: 1, 3, 5, 7 & 9, making up to 5 choices from the first digit to the fourth digit. thus, (5)(5)(5)(5)=5^4=625...

Let's call that number is abcd. We have 5 ways to choose odd number for each digit {1;3;5;7;9}. So the result is 5 5 5*5=625

Look at a 4 digit number like 4 empty spaces.

Each Empty space has a total capacity of 10, out of which 5 are odd numbers and 5 are even numbers, so the probability that a number is odd in an empty space is 1/2. There are 4 such spaces, each with an independent probability. The total probability of getting 4 odd numbers is 1/16.

1/16*100 = 6.25% there are 10000 numbers between 0 and 9999 (Including both 0 and 9999). 6.25% of 10000 = 625

there are 5 odd digits, 1, 3, 5, 7, 9 to form 4 digit odd number we can keep either of 5 digits in 100's, 10's and 1's place.

total numbers formed = 5 × 5 × 5 × 5 = 625

we know that there are 5 odd single-digit numbers (1,3,5,7,9)

and it is given that the number should be of four digits XXXX

Now, by using the fundamental principle of counting, we have, 5x5x5x5
--this means that there are 5 possibilities for each digit place that the number can be odd which are 1,3,5,7,9 (count=5)

now simply multiplying 5x5x5x5, we get,

625

which is the correct answer!

Since there are 5 odd digits, ( 1,3,5,7,9), we can arrange these digits in different ways to form a 4 digit numbers. In the number, we have 5 options for our 1st digit, second digit, 3rd digit and 4th digit because we can choose from any of the 5 digits(ex. 9999, 1357,1997) therefore, our answer is 5^4, or 625

From 0 to 10, there are 5 odd numbers, namely 1,3,5,7,9. And for our "odd looking" number we need all digit places in the 4 digit number to be odd. This means each digit place can be filled with any one of the five numbers, which gives a total of 5 ways to fill each digit place. Hence the total number of 4-digit distinct numbers is (5) (5) (5)(5) = 625.

5 odd digits (1 , 3 , 5 , 7 . 9) & "4-digit odds" so 5 x 5 x 5 x 5 = 625

An odd number is defined as the complement of an even number.

An even number "k" is a number that is wholly divisible such that k % 2 is 0.

An edge case of sorts is 0, which is defined as an even number. It fits the definition of an even number, and since the definition of the odd number is dependent on the even number, 0 cannot be an odd number. (This is in no way a rigorous proof - see http://en.wikipedia.org/wiki/Parity of zero)

Thus, for any given digit, we see that our choices are 1,3,5,7,9 - a total of 5 choices. There are 4 digits, each of which can be 1 of the 5 possible odd numbers. By the multiplication rule, we have 5^4 = 625 possible "odd-looking" 4-digit numbers.

All possible odd no. 1,3,5,7,9 a total of 5. No. of digits in the no. : 4 so each digit can have one of five no.s so no of combinations is 5^4 = 625

It's really easy. There are $5$ odd digits : $1,3,5,7,9$ So, each of the digits in the four-digit number can have one of these values. So, the sum of the possible cases is $5 \cdot 5 \cdot 5 \cdot 5 = 625$

There are 5 odd numbers: 1, 3, 5, 7, 9. Each of them could be one of the 4 digits. So the total possibles combinations is $5^{4}$ = $\boxed{625}$

There are four digits in an odd looking number. Each digit has 5 possibilities: 1, 3, 5, 7, and 9. Therefore the number of 4-digit odd looking numbers is $5^{4}$ or 625.

= 5^4

There are 5 different odd digits and each one could be in every place of the 4-digit number. To find how many "odd looking" numbers there are, you multiply 5 X 5 X 5 X 5 , a five for each digit. This is the same as writing out 1111, 1113, 1115 .... 9997, 9999, but it is much quicker.

There are 5 different odd digits $(1,3,5,7,9)$ . This means that there are $5$ choices for each digit spot. Since there are 4 digit spots, the answer is thus $5\times 5\times 5\times 5=\boxed{625}$ .

Odd Numbers are five -1,3,5,7,9.... Each digit of the desired number can be filled by all these five numbers. Hence Number of 4 digit odd looking numbers can be calculated as = 5^4 = 625

Since there are 5 odd numbers i.e. 1, 3, 5, 7 and 9 and there are no limitations on the order of the odd numbers for each four digit number, we can say that each of 5 odd digits can be used at the same time.

5^4=625

There are 5 odd numbers in the set of first 10 natural numbers. So, for 4 digit numbers, the answer is 5^4=625

There are only $5$ odd digits, namely $1,3,5,7, \& \ 9$ . Thus, the 4-digit numbers have to have only these 5 digits. Thus, there are $5^4$ possibilities (5 digits, 4 places) and the final answer is $\boxed{625}$ .

We know if 4-digits have 4 place that it can placed by 1,3,5,7,and 9 --> 5 odd numbers. Because it odd numbers can same in every places so, there are 5 x 5 x 5 x 5 = 625. ANSWER : 625

There are $5$ odd possible digits for each digit, hence $5^4 = \boxed{625}$ .

all the places to be acquired by odd numbers(5)so 5 5 5*5=625