| Author | Maths Problems |
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Hello,
I again invite you to send me the toughest of maths problems in simple syllabus. The winner will get x*50 gold, where x is the number of problems I get. The winner is decided bi-weekly.
Example -
If I get 100 problems, then the one who sends the best problem (It is not important whether I solve it or not) will get 5000 gold. |
1. One day, a person went to horse racing area, Instead of counting the number of human and horses, he instead counted 74 heads and 196 legs. Yet he knew the number of humans and horses there. How did he do it, and how many humans and horses are there?
Answer
2. y = log x
If y = 10, then what is x?
Answer
3. 10*9*8*7*6*5*4*3*2*1 = 10!
Can this be true?! Why or why not?
Answer
4. If 1/2x +1/2(1/2x + 1/2(1/2x +1/2(1/2x + ... = y,
then x = ?
Answer
5. What place in this world can have their temperatures Fahrenheit and Celsius equal?
Answer
6. If x*x + 2x - 35 = 0,
then x = ?
Answer
7. If ax*x + bx +c = 0,
then what is x?
Answer
8. What is the area of a regular hexagon with sides 1 in. long?
Answer
9. You have two block of clay in cube form and the edges are 10 cm. How many spheres with a radius of 5 cm can you make with that amount of clay?
Answer
10. Every month, a girl gets allowance. Assume last year she had no money, and kept it up to now. Then she spends 1/2 of her money on clothes, then 1/3 of the remaining money on games, and then 1/4 of the remaining money on toys. After she bought all of that, she had $7777 left. Assuming she only gets money by allowance, how much money does she earn every month?
Answer |
Ahh, not such questions mate ;)
Earlier the winner used to be the ones who'd PM me only 1 question, but the one question was as big as 6-7 lines.
The questions need to be tricky and tough.
1.24 horses, 50 men.
2.Not sure.
3.Yes.
5.-40, don't know place.
6.5/-7
7.Same Q as above.
8,9,10 all again calculation types.
I'll PM you some example questions.
Please only PM me the questions. Here I only wish to post the winners, and the best 2 problems. |
1) 196 - 74* 2 = 48;
48 excessive legs means 24 horses. Thus 24 horses and 50 humans.
2) x = 10^10
3) True, it is 10 factorial.
4) x * (1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 ...) = y
x * ( approaching 1) = y
so x is almost y
5) C*1.8 + 32 = F with C = F
0.8*C + 32 = 0
C = -32/0.8
= -40
6) x^2 + bx +c = 0
(x+7)*(x-5) = 0
x = -7 or x = 5
7) (-b+sqrt(b^2-4*a*c))/(2*a) or (-b-sqrt(b^2-4*a*c))/(2*a)
8) a hexagon conssists of 6 equal triangles. Surface of a triangle is 1/2*l*h, thus we get 6*1/2*1*cos(pi/6)
9) 2 blocks with edges of 10 cm have a volume of 2000 cm3. A sphere with a radius of 5 cm requires 4/3*pi*5^3= 524 cm3. So you can make 3 spheres.
10) 1/2+1/2*1/3+1/2*1/3*1/4 = 17/24. Thus 7/24 = 7777. The total allowence was then 26.664 a year, thus 2222 per month. (ps, she doesnt "earn" it, she just receives it ;) |
You have two match cords. The time it takes for each match cord to burn out is 100 seconds, but you don't know if they burn with constant speed (you can't tear a match cord apart in the middle and say that you have 50s + 50s).
With these two match cords and a lighter - how do you measure 75 seconds? |
On a unidimensional axis with origin in 0 you are on position 1. Every step you take, you have 50% chances to go forward (+1) and 50% chances to go backward (-1) on the axis.
Right when you start this (so you are on position 1), what are the chances that you will eventually get to point 0? |
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| A lady buys 200rs worth of groceries from a shopkeeper. She hands him a 1000rs note. As the shop keeper doesnt have change, he goes to a neighbouring shop and gets change. He hands the lady 800rs and keeps the 200rs with himself. After a while the neighbouring shopkeeper comes and says that the note was duplicate and takes back the 1000rs he gave. How much loss does the shopkeeper have? |
in the christmas event, we have a vault which can be unlocked by 4 kinds of trinkets. we need 28 trinkets of all kinds in total, however we may get a lot of extra trinkets of the kind we don't need that much. as a result we need some more than 28 trinkets in total to unlock the vault. assume the chance we get each kind of trinkets is 1/4, and the initial demand of the 4 kinds of trinkets are given. the question is: how many trinkets(expectation) we need actually to unlock the vault?
i believe nobody can solve this hahaha |
for Majblomma:
lit the first cord in one end and lit the second cord in both ends, when the second cord burns out lit the other end of the first cord, when the first cord burns out it is 75s. |
for ParaLeul:
1 |
| RevolutionRebel: Right! |
for RevolutionRebel:
Haha, now I realized I changed the problem by mistake. The original problem was like this:
On a unidimensional axis with origin in 0 you are on position 1. Every step you take, you have 2/3 chances to go forward (+1) and 1/3 chances to go backward (-1) on the axis.
Right when you start this (so you are on position 1), what are the chances that you will eventually get to point 0?
I suppose if you did the first one you wouldn't have problems to do this too.
Still, as I changed the problem, it is interesting that you have 100% chances to reach 0, even if somebody would say that there is a chance that somebody will keep going to the right or maybe sometimes stay on place by Though this 100% chances comes from the infinity of steps. |
Interesting questions till now, any more?
Let me say again, the best are the ones involving simple maths/physics, but being tricky. |
for ParaLeul:
1/2
try my problem if you are good at probability theory. for anyone solved it analytically i give 3 promises (if not offended with game rules) |
another problem which is easier but interesting:
suppose you are on a bumpy train and you have a glass of water on the table.experience tell us that if the glass is empty, it is unstable and easy to fall. and it is still unstable if the water is full. it would be most stable only if it is "half-full". the question is: what is the accurate water line of this most stable case? given the height-density(weight/height) of the glass as p1 and of the water as p2. |
| I like the trinkets problem, but I'm not equipped with the proper math knowledge to solve that one. I don't even know how to calculate the expected number of trinkets in the extreme (and worst) case where you need 28 trinkets of the same kind, but shouldn't be too hard. Can someone provide a solution to that? |
ottoman empire time, padisah (= emperor) orders 10 gold pouchs eacy containing 10 gold coin of 10 grams.
sneaky (but stupid ?) jeweler steals 1 gram from only 10 coins, puts them all in one pouch. sadly, he got caught. summoned to royal court lead by padisah himself.
padisah wishes to give him a chance for old times sake (assuming 1 in 10th chance).
identical poaches are numbered. he is given a pair of scales along with all kind of weights to get a reading. BUT he is allowed to perform only one scaling. if he can determine faulty pouch, he will survive. he manages. how ? (hint: opening poaches allowed) |
A logical question to solve without pen and paper:
A sect of 50 people live by themselves on an island. Each midnight a ferry comes and each sect member lives by the rule to leave on the next ferry if and only if they have blue eyes. In fact they all have blue eyes but they have no means to see their own eyes and it is forbidden to talk about eye color.
One day a visitor comes to the island. He appears in front of everyone and speaks out: "I see a person with blue eyes". Each sect member is a perfect logician and has full knowledge on the others' ablities and eye color and on who leaves the island.
What happens? |
It can be considered as a function of required numbers of trinkets. It is easy to write down recurrence formula and solve it numerically, where the initial values are the expectations of negative binomial distribution. It seems difficult to have a genenal formula.
in the christmas event, we have a vault which can be unlocked by 4 kinds of trinkets. we need 28 trinkets of all kinds in total, however we may get a lot of extra trinkets of the kind we don't need that much. as a result we need some more than 28 trinkets in total to unlock the vault. assume the chance we get each kind of trinkets is 1/4, and the initial demand of the 4 kinds of trinkets are given. the question is: how many trinkets(expectation) we need actually to unlock the vault?
i believe nobody can solve this hahaha |
