Sports games

Pupils of the same school participated in district sports games. When dividing the teams into teams, it was found that in the case of the creative teams with four pupils, one pupil was remaining, five-member teams had two pupils, and six-member teams had three pupils remaining. How many pupils in this school attended games if one school could participate a maximum of 80 pupils?

Correct answer:

n =  57

Step-by-step explanation:

0 = 4×0 + 0 = 5×0 + 0 = 6×0 + 0
1 = 4×0 + 1 = 5×0 + 1 = 6×0 + 1
2 = 4×0 + 2 = 5×0 + 2 = 6×0 + 2
3 = 4×0 + 3 = 5×0 + 3 = 6×0 + 3
4 = 4×1 + 0 = 5×0 + 4 = 6×0 + 4
5 = 4×1 + 1 = 5×1 + 0 = 6×0 + 5
6 = 4×1 + 2 = 5×1 + 1 = 6×1 + 0
7 = 4×1 + 3 = 5×1 + 2 = 6×1 + 1
8 = 4×2 + 0 = 5×1 + 3 = 6×1 + 2
9 = 4×2 + 1 = 5×1 + 4 = 6×1 + 3
10 = 4×2 + 2 = 5×2 + 0 = 6×1 + 4
11 = 4×2 + 3 = 5×2 + 1 = 6×1 + 5
12 = 4×3 + 0 = 5×2 + 2 = 6×2 + 0
13 = 4×3 + 1 = 5×2 + 3 = 6×2 + 1
14 = 4×3 + 2 = 5×2 + 4 = 6×2 + 2
15 = 4×3 + 3 = 5×3 + 0 = 6×2 + 3
16 = 4×4 + 0 = 5×3 + 1 = 6×2 + 4
17 = 4×4 + 1 = 5×3 + 2 = 6×2 + 5
18 = 4×4 + 2 = 5×3 + 3 = 6×3 + 0
19 = 4×4 + 3 = 5×3 + 4 = 6×3 + 1
20 = 4×5 + 0 = 5×4 + 0 = 6×3 + 2
21 = 4×5 + 1 = 5×4 + 1 = 6×3 + 3
22 = 4×5 + 2 = 5×4 + 2 = 6×3 + 4
23 = 4×5 + 3 = 5×4 + 3 = 6×3 + 5
24 = 4×6 + 0 = 5×4 + 4 = 6×4 + 0
25 = 4×6 + 1 = 5×5 + 0 = 6×4 + 1
26 = 4×6 + 2 = 5×5 + 1 = 6×4 + 2
27 = 4×6 + 3 = 5×5 + 2 = 6×4 + 3
28 = 4×7 + 0 = 5×5 + 3 = 6×4 + 4
29 = 4×7 + 1 = 5×5 + 4 = 6×4 + 5
30 = 4×7 + 2 = 5×6 + 0 = 6×5 + 0
31 = 4×7 + 3 = 5×6 + 1 = 6×5 + 1
32 = 4×8 + 0 = 5×6 + 2 = 6×5 + 2
33 = 4×8 + 1 = 5×6 + 3 = 6×5 + 3
34 = 4×8 + 2 = 5×6 + 4 = 6×5 + 4
35 = 4×8 + 3 = 5×7 + 0 = 6×5 + 5
36 = 4×9 + 0 = 5×7 + 1 = 6×6 + 0
37 = 4×9 + 1 = 5×7 + 2 = 6×6 + 1
38 = 4×9 + 2 = 5×7 + 3 = 6×6 + 2
39 = 4×9 + 3 = 5×7 + 4 = 6×6 + 3
40 = 4×10 + 0 = 5×8 + 0 = 6×6 + 4
41 = 4×10 + 1 = 5×8 + 1 = 6×6 + 5
42 = 4×10 + 2 = 5×8 + 2 = 6×7 + 0
43 = 4×10 + 3 = 5×8 + 3 = 6×7 + 1
44 = 4×11 + 0 = 5×8 + 4 = 6×7 + 2
45 = 4×11 + 1 = 5×9 + 0 = 6×7 + 3
46 = 4×11 + 2 = 5×9 + 1 = 6×7 + 4
47 = 4×11 + 3 = 5×9 + 2 = 6×7 + 5
48 = 4×12 + 0 = 5×9 + 3 = 6×8 + 0
49 = 4×12 + 1 = 5×9 + 4 = 6×8 + 1
50 = 4×12 + 2 = 5×10 + 0 = 6×8 + 2
51 = 4×12 + 3 = 5×10 + 1 = 6×8 + 3
52 = 4×13 + 0 = 5×10 + 2 = 6×8 + 4
53 = 4×13 + 1 = 5×10 + 3 = 6×8 + 5
54 = 4×13 + 2 = 5×10 + 4 = 6×9 + 0
55 = 4×13 + 3 = 5×11 + 0 = 6×9 + 1
56 = 4×14 + 0 = 5×11 + 1 = 6×9 + 2
57 = 4×14 + 1 = 5×11 + 2 = 6×9 + 3




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