Spartakiada

Practitioners lined up in rectangle with row with four, five or six exercisers, one always missing to full rectangle. How many exercisers were on the field, if they have estimated not been more than 100?

Correct result:

n =  59

Solution:

$$\begin{gathered} 4=2^2 \\ 5\mathrm{.}\mathrm{.}\mathrm{.}primenumber \\ 6=2\cdot 3 \\ LCM(4,5,6)=2^2\cdot 3\cdot 5=60 \\ n=LCM(4,5,6)-1=59 \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• The florist
  A consignment of 200 roses arrived at the florist in the morning. She sold more than half of them during the day. She wants to tie bouquets of the remaining roses. If she ties a bouquet of three, four, five or six roses, there will always be one rose left
• Athletes
  Athletes at the stadium could enter two-steps, three-steps, four-steps, five-steps, six-steps. There were more than 100 but less than 200. How many athletes were there?
• The florist
  The florist had 200 roses in the morning. During the day, more than half sold it. From the remaining roses, it will tie the bouquet. If a bouquet of 3, 4, 5 or 6 roses are bound, one always remains. How many roses from the morning shipment sold?
• Dance group
  The dance group formed groups of 4, 5, and 6 members. Always one dancer remains. How many dancers were there in the whole group?
• Three friends
  Three friends had balls in ratio 2: 7: 4 at the start of the game. Could they have the same number of balls at the end of the game? Write 0, if not, or write the minimum number of balls they had together.
• Four classses
  Students of all 7, 8 and 9 classes in one school may take up 4,5,6 and 7 abreast and nobody will left. How many is the average count of pupils in one class if there are always four classes each grade?
• Shepherd
  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?
• Bouquet
  Gardener tying bouquet of flowers for 8 and none was left. Then he found that he could tying bouquet of 6 flowers and also none was left. How many have gardener flowers (minimum and maximum) if they had between 50 and 100 flowers?
• Fewer than 500 sheep,
  There are fewer than 500 sheep, but if they stand in a double, triple, quadruple, five and sixth order, one sheep will remain. But they can stand in the seventh order. How many are sheep?
• Sheep
  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?
• Dance ensemble
  The dance ensemble took the stage in pairs. During dancing, the dancers gradually formed groups of four, six and nine. How many dancers have an ensemble?
• Summer camp
  Some boys or girls signed up for the summer camp, which has a maximum capacity of 200 children. The main leader noticed that during the evening start, he could arrange the participants exactly in the twelve-step, sixteen-step, or eighteen-step, and no one
• Dining tables
  In the dining room are tables with 4 chairs, 6 chairs, 8 chairs. How many diners must be at least to be occupy all tables (chairs) and diners are more than 50?
• Meadow
  On the meadow grazing horses, cows and sheep, together less than 200. If cows were 45 times more, horses 60 times more and sheep 35 times more than there are now, their numbers would equall. How many horses, cows and sheep are on the meadow together?
• Package
  The package has no more than 66 m of cloth. If we just cut it all on the blouses or all on dresses, no cloth left remain. On the one blouse consumes 1.3 m of cloth and on one dress 5 m. Determine the amount of the cloth in the package.
• Tiles
  How many tiles of 20 cm and 30 cm can build a square if we have a maximum 100 tiles?
• Plum
  On the platter are plum. How many were there if its have to be able to share equally among 8,10 and 12 children?