Question 1146503
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I understand the problem in <U>THIS WAY</U> :


<pre>
     There is a set of cards.

     If they are distributed equally between 2 persons, 1 card  is  leftover.

     If they are distributed equally between 3 persons, 2 cards are leftover.
   
     If they are distributed equally between 4 persons, 3 cards are leftover.

     If they are distributed equally between 5 persons, 4 cards are leftover.

     If they are distributed equally between 6 persons, 5 cards are leftover.

     If they are distributed equally between 7 persons, NO cards are leftover.

     Find the minimum amount of cards to satisfy the above conditions.
</pre>


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>SOLUTION</U>


<pre>
Let N be the number under the question.


Add (mentally) 1 card to the set of cards. In other words, consider the number N+1.


Then it is divisible by 2; by 3; by 4; by 5 and by 6.


The minimal such a number is  60.


Check then, if  N-1 = (60-1) = 59 is divisble by 7.   ----- It is not divisible.


Next number to try is 60*2 = 120.


Check if 120-1 = 119 is divisible by 7.  ----- You are LUCKY: it is (!).


So the answer to the problem is  N = 119.
</pre>


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(&nbsp;!&nbsp;) &nbsp;<U>S O L V E D</U> &nbsp;(&nbsp;!&nbsp;)


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It is a standard problem of a school Math circle level (typically, for children starting from 5-th or 6-th grade).


See the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/divisibility/lessons/The-number-that-leaves-a-remainder-1-when-divided-by-2-by-3-by-4-by-5-and-so-on-until-9.lesson>The number that leaves a remainder 1 when divided by 2, by 3, by 4, by 5 and so on until 9</A>

in this site.


Find there a lot of similar problems, solved and explained to you.



When children attend such Math circles and solve there such problems under guidance of devoted and enthusiastic teachers, 
then there is a chance that they will love Math (and will learn on how to think mathematically) when they become adults . . . 



Then there is also a chance that they will pass this enthusiasm and the way of thinking to their own children 
and to next generations, in general . . .