# Examples for 9th grade - page 3

- Proof PT

Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it. - 7 heroes

5 heroes galloping on 5 horses behind. How many ways can sort them behind? - Vans

In how many ways can 7 shuttle vans line up at the airport? - Troops

Route is long 203 km and the first day first regiment went at an average speed 20 km/h and journey back 19 km/h. The second day went second regiment same route at an average speed 18 km/h there and back. Which regiment will take route longer? - Flags

How many different flags can be made from colors red, white, blue, black, yellow, green, purple, gray, orange so that each flag consisted of three different colors? - Seating

How many ways can 7 people sit on 3 numbered chairs (eg seat reservation on the train)? - Football league

In the 2nd football league is 19 teams. How many ways can be filled first, second and third place? - Guests

How many ways can 7 guests sit down on 9 seats standing in a row? - Stock market

Simon one day decided to invest € 88000 to the stock market. After six months he invested July 5 stock markets fell by 56%. Fortunately for Simon from July 5 5 to October 5 his shares have risen by 39%. Simon is then: ? - Candies

In the box are 12 candies that look the same. Three of them are filled with nougat, five by nuts, four by cream. At least how many candies must Ivan choose to satisfy itself that the selection of two with the same filling? ? - Logs

Trunk diameter is 72 cm. Is it possible to inscribe a square prism with side 54 cm? - Playing cards

How many possible ways are to shuffle 7 playing cards? - Series

Andrew wrote this series of numbers: 1,3,7,15, .... n. Which number in the series does not belong? ? - Shelf

How many ways are there to arrange 9 books on a shelf? - Ace

From complete sets of playing cards (32 cards) we pulled out one card. What is the probability of pulling the ace? - Sequence

Write the first 7 members of an arithmetic sequence: a_{1}=8, d=-9. - Logic

A man drinks a barrel of water for 31 days, woman for 58 days, for how many days they drink barrel together? - Trapezoid

Are diagonals in a rectangular trapezoid perpendicular and bisect the angles? - Medals

In how many ways can be divided gold, silver and bronze medal among 18 contestant? - Road

Between cities A and B is route 3 km long of rise average 4‰. Calculate the height difference of cities A and B.

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