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

n=3x+1 n=6y−1 3x+1=6y−1 3x−6y=−2 6y−3x=2;x,y∈N;P=∅  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 n = 3x+1 \ \\ n = 6y-1 \ \\ 3x+1 = 6y -1 \ \\ 3x - 6y = -2 \ \\ 6y - 3x = 2; x,y \in N; P = \emptyset \ \\ \ \\ 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 \ \\

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