The smallest multiple
Find the smallest positive multiple of nine containing only even digits.
The answer is 288.
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6 solutions
Note: I added "positive" to the problem statement, otherwise there is no solution.
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What about 36? I am somewhat confused
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is 3 even?
3 is not an even number .
36 has a digit 3 which is odd..though 6 is even
nice question :D
288 is fine!
What about 108. 12*9, is even...
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Is 1 even?
Note that all of the digits have to be even. Otherwise, the smallest answer would be 2 × 9 = 1 8 .
Wat bout 108
I reasoned as follows: The smallest multiple of 9 has to be a multiple of 18 because the number has to be even. All multiples of 18 < 200 contain an odd number, because all multiples of 18 are multiples of 9 and all multiples of 9 < 200 contain an odd number. So the first possibility is > 200. The first multiples of 18 > 200 are 216, 234, 252, 270, 288 which is your answer
I am I am not convinced with the fact that next smallest example should sum to 18 (even though it does) eg: 111111111111111111 is greater than 999
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That is a great point! Do you know how to fill the gap?
why not 90?
why not 54 ? isn't it the smallest multiple of 9 ? containing even digits ?
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5 is not even dude
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:( sorry :( I suck at everything -_-
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@Sifat Shishir – it's okay man. i also don't get this problem. hahaha.
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@Earl Stanley Leonardo – ALL the digits hafta be even.
In 54 5 is an odd digit
Whay about 90...
the smallest multiple is 32 * 9=288.
and the next answer would be 9 * 54=486
therefore answer is=288
Can you explain why you multiplied by 32?
This is wrong, the second answer is 468
2+8+8=18 (sum of digits of that number should be divisible by 9) and since 9 cannot be formed by adding even integers, so the next multiple is 18 and the digits that make 18 are 2,8,8 and hence 288 is the answer.
Start off with 9 and keep multiplying by two until you reach such a number.
i.e. 9 x 2 = 18, 18 x 2 = 36, 36 x 2 = 72, 72 x 2 = 144, 144 x 2 = 288.
288 is the answer.
The sum of the digits must be a positive even multiple of 9. 18 is the smallest example. Using only even digits we need 3 of them, eg. 666. In order to make the value as small as possible, decrease the first digit and increase the last by 2 to get 468. Continue to transfer value to less significant digits to get 288.
I am not convinced with the fact that next smallest example should sum to 18 (even though it does) eg: 111111111111111111 is greater than 999
Moderator note:
0 is not a positive number.
0 is not positive.
In future, if you spot any errors with a problem, you can “report” it by selecting "report problem" in the menu. This will notify the problem creator who can fix the issues.
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We have that : 0 ≥ 0
So we should probably say stricly positive
why cant it be 54
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I just can't see how 5 is even ?
If a number is divisible by nine then the sum of digits must be a multiple of nine.
But if all of the digits are even then they must sum to an even multiple of nine, and the smallest even multiple of nine is eighteen.
Hence we are looking for the most efficient way to write eighteen as the sum of even digits: 2 + 8 + 8 . That is, the smallest multiple of nine containing only even digits is 2 8 8 .