Maths Puzzlers

[toonmilo]

1. A baseball team has just won the championship and the players want to congratulate each other. They began shaking hands with every other player just once.There are 9 players in a baseball team. How many times did the players shake hands?

2.A jar has 4 ameobas in it to start. Amoebas split their cells in two (doubling in size) once every minute. The jar will be completely filled in ten minutes. How long would it take to fill the exact same jar if there were 8 ameobas in it at the start?

3. There are 100 golfers in the local match play contest.If a player loses a match he is immediatley eliminated from the contest. How many matches will be played to determine the winner?

4. 2 trains are ona head on collision course.The trains currently 65 miles apart. The North Bound train is travelling at 55 mph and the south bound train is travelling at 80 mph. What is the distance between the trains 2 minutes before they collide?

5. Find a simple method of solving:- 6751X + 3249Y = 26751 and 3249X + 6751Y = 23249

6.2 friends decide to get together, so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 mph. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start travelling, the pigeon flies back and forthe at 18 mph between the 2 friends until the friends meet. How far does the pigeon travel?

[Gnu]

1.  Each of the 9 people shake hands with 8 others i.e. 72 handshakes.  However, this counts every combination twice, so the answer is 36.

2.  9 minutes, as 8 amoeba is the position after 1 minute of the original problem.

3.  99.  Each match eliminates one person.

4.  The closing speed is 135mph, so in two minutes they travel 2/60 x 135, or 4.5 miles.

6.  The friends take 3 hours to meet, so the pigeon flies for 3 hours at 18mph, which is 54 miles.

[Gnu]

5.  Using algebra, and because the numbers are the same, you can subtract one from the other to give

6751(x - y) - 3249(x - y) = 26751 - 23249

so

3502(x - y) = 3502

x - y = 1

i.e. x = y + 1

in the orginal equation

6751(y + 1) + 3249y = 26751

10000y + 6751 = 26751

or y = 2 and so x = 3

 

I'm not sure if that is easy enough, but it works!

[Better2try]

5. x = 3 and y = 2.  Adding together both equations gives 10000x + 10000y = 50000 or.... 

                                    x+ y = 5

Now, it's easy !

[Better2try]

1. 36 handshakes required.

   9 players shake 8 others = 72 handshakes. This simple rule counts A shaking B's hand AND B shaking A's hand. Same players with 2 handshakes. So, if only one handshake allowed between players, total = half of 72 = 36.

[Better2try]

2.9

[Cobalt272]

1. 45 handshakes

9+8+7+6+5+4+3+2+1 = 45

first person shakes once with 8 other people

the next person now has 7 people to shake hands with since he has already shaken with the first person

the next person now has 6 people to shake hands with since he has already shaken with the first 2 people

etc

[mldr79]

Cobalt it is 36 as already stated, not 45.

If the first person shakes 8 hands, the subsequent person shakes 7 as he has already shook person 1 (as you say) then the sum is 8+7+6+5+4+3+2+1=36. There is no 9 to add as no one person shakes 9 hands.