Question 53086
.
My daughter got this word problem for school and it sounds pretty simple to me 
but I have tried everything and I am horrible at math so I need a little help 
before I throw my calculator out the window! Here is it

Linae went shopping for Kou-jong tiles at the local toy shop the other day. 
The kou-jong tiles were on sale for only 28 cents each.
However, she got it in her head that, for good luck, the total amount of money 
she must spend must be a number where all of the digits are the same.

With that in mind, what is the minimum number of tiles she must buy?
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        The solution by @consc198 in his post is, OBVIOUSLY, wrong and irrelevant.

        For a correct solution see what follows.



<pre>
We want to have a positive integer number (the spent amount) where all the digits are the same,
and this number should be multiple of 28. The additional condition is that this number must be minimal possible.


Since this number is a multiple of 28, it should be a multiple of 4 and a multiple of 7.

It means that we should find a minimum possible number written by ones, '1', which is a multiple of 7.


Make "trial and error".


111 divided by 7 gives the remainder 6.

1111 divided by 7 gives the remainder 5.

11111 divided by 7 gives the remainder 2.

111111 divided by 7 gives the remainder 0: in other words, 111111 is a multiple of 7.


It implies that 444444 is a multiple of 28.


Thus the minimum number of tiles Linae should buy to satisfy the conditions is 444444/28 = 15873.


<U>ANSWER</U>.  The minimum number of tiles Linae should buy to satisfy the conditions is 15873.
</pre>

Solved.