Sports games

Pupils of same school participated district sports games. When dividing into teams found that in the case of the creation teams with 4 pupils remaining 1 pupil, in the case of a five-member teams remaining 2 pupils and in the case of six-members teams remaining 3 pupils. How many pupils in this school attended games if one school could participated a maximum of 80 pupils?

Result

n =  57

Solution:

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

Solution in text n =







Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Next similar examples:

  1. Children
    car_game Less than 20 children is played various games on the yard. They can create a pairs, triso and quartets. How many children were in the yard when Annie came to them?
  2. Four-digit number
    numbers_1 Find also a four-digit number, which quadrupled written backwards is the same number.
  3. The balls
    balls_4 You have 108 red and 180 green balls. You have to be grouped into the bags so that the ratio of red to green in each bag was the same. What smallest number of balls may be in one bag?
  4. Tissues
    harmasan The store got three kinds of tissues - 132 children, 156 women and 204 men. Tissues each species were packed into boxes after the number of pieces the same for all three types (and greatest). Determine the number, if you know that every box has more than 6
  5. Divisibility
    numbers_29 Write all the integers x divisible by seven and eight at the same time for which the following applies: 100
  6. Sheep
    ships Shepherd tending the sheep. Tourists asked him how much they have. The shepherd said, "there are fewer than 500. If I them lined up in 4-row 3 remain. If in 5-row 4 remain. If in 6-row 5 remain. But I can form 7-row." How many sheep have herdsman?
  7. Divisors
    divisors The sum of all divisors unknown odd number is 2112. Determine sum of all divisors of number which is twice of unknown numbers.
  8. Grandmother
    cukriky_3 Grandmother wants to give the candies to grandchildren that when she gives 5 candy everyone 3 missing and when she gives 4 candies 3 is surplus. How many grandchildren has grandmother and how many candies has?
  9. Remainder
    numbers2_35 A is an arbitrary integer that gives remainder 1 in the division with 6. B is an arbitrary integer that gives remainder 2 the division by. What makes remainder in division by 3 product of numbers A x B ?
  10. Divisibility by 12
    numbers2 Replace the letters A and B by digits so that the resulting number x is divisible by twelve /find all options/. x = 2A3B How many are the overall solutions?
  11. Lines
    bus Five bus lines runs at intervals 3, 6, 9, 12, 15 minutes. In the morning, suddenly start at 4:00. After how many minutes the bus lines meet again?
  12. Shepherd
    sheep_1 The shepherd has fewer than 500 sheep; where they can be up to 2, 3, 4, 5, 6 row is always 1 remain, and as can be increased up to 7 rows of the sheep, and it is not increased no ovine. How many sheep has a shepherd?
  13. Trees
    trees_1 Loggers wanted to seed more than 700 and less than 800 trees. If they seed in rows of 37, left them 8 trees. If they seed in rows of 43, left the 11 trees. How many trees must seed ?
  14. Divisors
    one Find all divisors of number 493. How many are them?
  15. Digit sum
    numbers_41 Determine for how many integers greater than 900 and less than 1,001 has digit sum digit of the digit sum number 1.
  16. Divisible by 5
    175px-5th_MarDiv How many three-digit odd numbers divisible by 5, which are in place ten's number 3?
  17. Decomposition
    prime_factorization Make decomposition using prime numbers of number 155. Result write as prime factors (all, even multiple)