Group

Group of kids wanted to ride. When the children were divided into groups of 3 children 1 remain. When divided into groups of 4 children 1 remain. When divided into groups of 6 children 1 missed. After divided to groups of 5 children its OK. How many are there?

Correct result:

n =  0

Solution:

Problem has no solution

$$\begin{gathered} n=3x+1 \\ n=6y-1 \\ 3x+1=6y-1 \\ 3x-6y=-2 \\ 6y-3x=2;x,y\in N;P=\mathrm{\varnothing } \\ d3:4,7,10,13,16,19,22,25,28,31,34,37,40,43,46,49,52,55,58,61,64,67,70,73,76 \\ d4:5,9,13,17,21,25,29,33,37,41,45,49,53,57,61,65,69,73,77,81,85,89,93,97,101 \\ d6:5,11,17,23,29,35,41,47,53,59,65,71,77,83,89,95,101,107,113,119,125,131,137,143,149 \\ d5:5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100,105,110,115,120,125 \\ d3:10,25,40,55,70,85,100,115,130,145,160,175,190,205 \\ d4:5,25,45,65,85,105,125,145,165,185,205,225,245,265 \\ d6:5,35,65,95,125,155,185,215,245,275,305,335,365,395 \end{gathered}$$

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