Math Trivia2

8/2/2019 Math Trivia2

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SUBMITTED BY:

KENETH ADLAWAN

RICA ANN

BONGHANOYLYNDELLE

ARRIESGADO

PEA JANE LIMORAN

FRESHLYPARAGUSO

SUBMITTED TO:

MR.

ELMER


2/23

QUESTION #1

A soccer team just became first in the nationalleague. The players which were on the field justafter the referee blew the final signal wanted to

congratulate each other by shaking hands.Assuming that each player shook hands withevery other player only once, how many time were

the hands shaken in total? (There are of course 11players in a soccer team)


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SOLUTION AND ANSWER

SolutionJust name the players 1, 2, 3, .... and 11. Player 1 has to

shake hands with player 2, 3, ... and 11. So this countsfor 10 shakes.

Player 2 has already shaken hands with player 1. He stillhas to shake hands with player 3, 4, ... and 11. So thiscounts for 9 shakes.

So continuing, player 3 has now to shake still 8 times,

then player 4 7 times,So in total hands were shaken10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 =

Answer:

=55 times.


4/23

Question #2

A hiker walked for two days. On the second day thehiker walked 2 hours longer and at an averagespeed 1 mph faster than he walked on the first

day. If during the two days he walked a total of 64miles and spent a total of 18 hours walking, whatwas his average speed on the first day?


5/23

ANSWER AND SOLUTION

Solution

When t=time and s=speed:

t1 + t2 = 18 and t2 = t1 + 2, from which t1 = 8 and t2 = 10

s2 = s1 + 1 and s1 * t1 + s2 * t2 = 64so 8*s1 + 10*(s1+1) =

ANSWER:

64, from which s1 = 3


6/23

QUESTION #3Today, John has to transfer 50 euro to the bank

account of a Dutch friend. He has written down theaccount number on a piece paper. But since he hadforgotten to take out the paper from his trouserswhen he put them in the washing machine, one digit

of the bank account number became unreadable.The note says: 3170?4847. The friend of John isclimbing the Mount Everest at the moment, so it isimpossible for John to call his friend. Suddenly heremembers that a for a valid Dutch bank accountnumber it holds that the first digit times 9 + thesecond digit times 8 + the third digit times 7 + ...... +the nineth digit times 1 should be divisible by 11.John thinks for a moment and finds the correct

number. What is it?


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ANSWER AND SOLUTIONSolution

Let us call the unreadable number x. The bank accountnumber is hence 3170x4847.

The first digit times 9 + the second digit times 8 + thethird digit times 7 + ...... + the nineth digit times 1should be divisible by 11. So 27 + 8 + 49 + 0 + 5*x + 16+ 24 + 8 + 7 should be divisible by 11, in other words139 + 5 * x should be divisible by 11. Since 132 = 11*12it follows that 7 + 5 * x should be divisible by 11. That

only works if x = 3.

ANSWER:

Hence the correct bank account number is317034847.


8/23

QUESTION #4

Bob buys two things in a shop. With his pocketcalculator he calculates in advance what he has topay: 5.25 dollars. But what he does not notice isthat he pressed the division instead of the additionbutton. At the desk he is not surprised if he hearsthat he has to pay 5.25 dollars. What is the priceof the two things Bob has bought?


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ANSWER AND SOLUTIONSolution:

Let us call the two prices of the things x and y.According to Bob's (wrong) calculation: x / y = 5.25

According to the shop x + y = 5.25.

From the first equation it follows that x = 5.25*y. Plugginthis into the second equation gives that

6.25 * y = 5.25.

This gives y = 0.84 and x = 4.41.

Answer:

So the things Bob has bought costed 0.84 and 4.41

dollars.


10/23

QUESTION #5

A sultan has 14 daughters. He decides totell every night four of his daughters a

fairy tale, but in such a way that everynight, there will be another combinationof four daughters. How many nights will

keep the sultan busy telling fairy tales?


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Answer and Solution

Solution:Name the daughters of the sultan A,B,C,..., I. On a

particular day the sultan can choose in 14 * 13 * 12 *11 ways 4 daughters. In total this are 24024

combinations. But some of the combinations areequalt, that is if for example A, C, D, and F arelistening to a fairy tale, this is the same as F, C, D, andA. There are 4 * 3 * 2 * 1 = 24 permuations which areequal. So in total the X ere are 24024 / 24 = 1001distinct combinations.

Answer:The sultan will hence tell fairy tales for 1001 nights.


12/23

QUESTION #6

A wire with a length of 60 meter is hanging betweentwo high voltage pylons. The wire is connected tothe pylons at a height of 50 meters. The middle

part of the wire is 20 meters above ground level.How far are the high voltage pylons standingapart?

ANSWER AND


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ANSWER ANDSOLUTIONSolution:

because the length of the wire is exactlyenough to go down from one pylon to thelowest point (30 meter) and up again (30

meter).

Answer:

0 meter


14/23

QUESTION #7

If you would fold a letter in two fiftytimes, how thick should the envelopebe that can fit the letter? Assume that

the thickness of a piece of paper isabout 0.05 mm.


15/23

ANSWER AND SOLUTION

ANSWER: Compare this to he distance betweenthe earth and the sun which is about 150

million kilometers!

Solution

1st time folding: 0.05 x 2 = 0.1 mm

2nd time folding: 0.1 x 2 = 0.2 mm

3rd time folding: 0.2 x 2 = 0.4 mm...

50st time folding: 2 to the power 50 times 0.05mm.


16/23

QUESTION #8

A high school has as strange principal. On the first day,he has his students perform an odd opening dayceremony:

There are one thousand lockers and one thousandstudents in the school. The principal asks the firststudent to go to every locker and open it. Then he hasthe second student go to every second locker and

close it. The third goes to every third locker and, if it isclosed, he opens it, and if it is open, he closes it. Thefourth student does this to every fourth locker, and soon. After the process is completed with the

thousandth student, how many lockers are open?


17/23

ANSWER ANDSOLUTIONSolution:

The only lockers that remain open are perfect squares (1, 4,

9, 16, etc) because they are the only numbers divisible byan odd number of whole numbers; every factor other thanthe number's square root is paired up with another. Thus,these lockers will be "changed" an odd number of times,which means they will be left open. All the other numbers

are divisible by an even number of factors and willconsequently end up closed.So the number of open lockers is the number of perfect

squares less than or equal to one thousand. Thesenumbers are one squared, two squared, three squared,four squared, and so on, up to thirty one squared. (Thirtytwo squared is greater than one thousand, and thereforeout of range.)

ANSWER:So the answer is thirty one.


18/23

QUESTION #9A long and straight row of soldiers is marching with

constant speed. The dog of the commander runsalong the row from the end till the beginning, fromthe beginning till the end, from the end till thebeginning etc. This takes always 2 minutes, 1

minute, 2 minutes, etc.At some point the soldiers have to pass a very small

bridge. However, the commander does not trustthe strength bridge completely. He wonders how

much time it will take them to pass the bridgewhen they stay marching with the same speed.

How much time is that?


19/23

ANSWER AND SOLUTIONSolution:

It takes the dog 1 minute to run from the first to the last man.Then he runs 2 minutes from the last to the first man andthen 1 minute back from the first man to the last man. Sosince the dog ran 2 minutes in both directions, after 4

minutes he is at the same point where he was 4 minutesago. Since 4 minutes ago he was at the beginning of therow, and now he is at the end, this implies that it takes themarching soldiers 4 minutes to pass a point. So since thebridge was very small

ANSWER:

they will also pass it in 4 minutes.

QUESTION 0


20/23

QUESTION #10

A very rich lady goes with a bag of coins (notmore than 400) to the city. In the city she meetsfour vagabonds. She gives the first vagabond 4coins and a quarter of the number of coins

which is left in the bag. She applies the sameprocedure to the second, third and fourthvagabond (so division by 4 worked always).

With how many coins did she leave home?

ANSWER AND SOLUTION


21/23

ANSWER AND SOLUTION

ANSWER:= 256 coins. But since we "borrowed" 12 coins, in reality the ladybrought 256 - 12 = 244 coins to the city. (the other possibilities

are 500, 756, ....)

SOLUTION:

There are many ways to solve this problem. But there

is at least one simple way to solve it. Suppose thatthe lady starts with 40 coins. The first vagabondgets 4 and 1/4 * 36 = 9, in total 13 coins. You wouldhave found this number 13 immediately if the ladyhad brought 12 coins in addition (52) and thendivided by four! This implies that if the lady brings12 coins in addition, she had be able to divide 4times by 4 without a remainder. So she should have

brought 4 * 4 * 4 * 4


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Math Trivia2