• Lobby

  • Hard Riddles and Math exercices

9. Difficulty 1/5
If..
1=5
2=25
3=325
4=4325
then
5=?




10. Difficulty 1/5

The image is not on the scale
The side of the square and the circumference of the circle are equal.
We are rolling the circle on the square (like a wheel) how many complete tours will the circle make f it has rolled all over the square and came back to its original place?




11. Difficulty 2/5
for any x different from 0 => 0^x=0
for any x different from 0 => x^0=1

what is lim x->0 (x^x) ??
show all steps
@xterm correct

12. Difficulty 2/5
we have 10 bags.
Each bag contains 100 coins, every coin weighs exactly 10 grams.
One of the bags has bad coins, each of its coins weighs 11 grams.
with a precision balance scale how can you identify the bag which contains the bad coins?
We can use the balance only once (you can't add 1 coin at a time, you have to put them all together to read the measure once)

13. Difficulty 3/5
You have 1 bar of gold you need to pay a servant for 7 days. Each day you have to pay him the same amount and you put them in a safe which he will take when he finishes work after 7 days.
What is the minimum number of cuts you need to make to the gold bar to make all the transactions?

Edit:
There is still #3 - 7 - 10 - 11 - 12 and 13 that were not solved... If you have good riddles share them too
7) i'm not sure if it's correct, i've added one stroke to the plus sign to make it look like a 4.
545 + 5 = 550
Is there anything missing from #12? Shouldn't the riddle limit the number of tries? I'm not sure if I completely understand it but it's just a matter of trying each bag until you stumble upon a bag with a weight greater then 1KG.


#13 .. why do I need to cut the bar of gold? He will take it after 7 days and I don't have to pay him on daily basis.
@m0ei correct

@ali no you have to use the balance only once... sorry i didn't put that and #13 just for the riddle to work
12.
Collect n coins from bag n where n 1->10
you now have 55 coins, weigh them, let the reading be W
subtract W - 550 = X
bag number X would be the bag with bad coins.
MSD wrote12.
Collect n coins from bag n where n 1->10
you now have 55 coins, weigh them, let the reading be W
subtract W - 550 = X
bag number X would be the bag with bad coins.
correct
I still don't get the question 13
I guess no one will be able to solve 3. So i'm going to post all 8 solutions:

1. Draw segment DF parallel to BC with F on AB. Draw CF intersecting BD at G.
Now find the equilateral triangles and isosceles triangles.
2. Use the Law of Sines in triangle BED and triangle BCD. Use BE = BC to connect
the results. Simplify and solve for 6 EDB.
3. Draw lines through D and B parallel to BC and DC, respectively, intersecting at H.
Draw CG with G on BD and 6 GCB = 60. Show E is the incenter of triangle BDH.
4. Mark K on AC such that 6 KBC = 20. Draw KB and KE. Show BE = BC =
BK = KE = KD.
5. (Maria Gelband) Reflect E through AC to point H. Show D is on the circumcircle of
triangle BEH.
6. (Sergei Saprikin) Let the bisector of 6 ABC intersect AC at point T. Show D is an
excenter of triangle BET.
7. (Alexey Borodin) Let O be the circumcenter of triangle DEC. Show BD is the perpendicular
bisector of EO.
8. (Alexander Kornienko) Reflect triangle ABC through AB to triangle ABC0 and also
relect it through AC to triangle ACB0. Show that C0, E, and D are collinear.
Let me put it this way:
You are playing a gambling game with a bar of gold that weighs 7 Kg.
Each time you loose you give the your opponent 1 Kg of gold.
Assuming that their is only you and one other person playing and the other person starts with zero gold.
You lost the first time, you give him 1K... and so on
What if you lost 7 times in a row, and each time your opponent's gold increases by 1 Kg... how many minimum cuts do you cut your gold bar to complete the transactions?
I hope it's clearer now
13. Uhhhh 6 ? #|#|#|#|#|#|# (Unless you're presuming that you only pay him after the 7th win, meaning you just don't cut)
xterm wrote13. Uhhhh 6 ? #|#|#|#|#|#|# (Unless you're presuming that you only pay him after the 7th win, meaning you just don't cut)
No after each loss you must give him 1 K, and 6 cuts is the maximum number of cuts... think again
So there is a chance you would not pay him at all?
Ra8, could you please inform us of the way used to solve number 8 ?
13. 2 times, cut the bar of gold into three pieces where the size of the smallest is x/7 where original size of bar is x. The other 2 pieces are of sizes 2x/7 and 4x/7. The first day you give the store owner piece of size x/7. The next day the piece with size 2x/7 where he'll give you back the one with size x/7. The 3rd day give him the piece of size x/7, and the 4th day give him the piece of size 4x/7 where he'll give back the 2 pieces of sizes x/7 and 2x/7. 5th day give him the piece of size x/7, and 6th day give him the piece of size 2x/7 where he'll give back the one with size x/7. Last day give him the last piece with size x/7.

Riddle

Remove half of five to obtain four.
@mesa177 answer to your riddle is: F(IV)E remove F and E ---> IV :)

Riddle:
Difficulty: 1/5
Complete the sequence: 1=3, 2=3, 3=5, 4=4, 5=4, 6=3, 7=5, 8=5, 9=4, 10=3, 11=?, 12=?
@ mesa #13 correct
@mahmoud it's the 7th line of pascale's Triangle
EddieEC wrote@mesa177 answer to your riddle is: F(IV)E remove F and E ---> IV :)

Riddle:
Difficulty: 1/5
Complete the sequence: 1=3, 2=3, 3=5, 4=4, 5=4, 6=3, 7=5, 8=5, 9=4, 10=3, 11=?, 12=?
Eleven = 6, Twelve = 6

CHARACTERS

EDIT: I find such riddles not so accurate since it depends on someone expecting the answer to be relevant to the spoken language, which makes it more of a language riddle than a math riddle.
guys is there a place you're getting these riddles from? I'd love a place full of riddles.
Thanks.

Riddle #E1:
Difficulty: 2/5
One day your minimalist friend is visiting, and she presents you with the numbers 2, 3, 4 and 5, and the symbols = and +, and the following tantalizing challenge: It is possible to use each number and symbol once and only once and end up with a true equation; further, you cannot use any number or symbol not given. How can you do this?

Riddle #E2:
Difficulty: 4/5
There are four men who want to cross a bridge. They all begin on the same side. You have 17 minutes to get all of them across to the other side. It is night. There is one flashlight. A maximum of two people can cross at one time. Any party who crosses, either one or two people, must have the flashlight with them. The flashlight must be walked back and forth, it cannot be thrown, etc. Each man walks at a different speed. A pair must walk together at the rate of the slower man

Man 1: 1 minute to cross
Man 2: 2 minutes to cross
Man 3: 5 minutes to cross
Man 4: 10 minutes to cross

For example, if Man 1 and Man 4 walk across first, 10 minutes have elapsed when they get to the other side of the bridge. If Man 4 returns with the flashlight, a total of 20 minutes have passed, and you have failed the mission.

Riddle #E3:
Difficulty: 3/5
There are three boxes. One has apples, one has oranges and the other has apples and oranges. The boxes are labeled wrong so that no label is correct. Sue opens just one box, and without looking in the box, takes out one piece of fruit. She looks at the fruit and immediately labels all the boxes correctly. Which box did she open and how did she know?
Not a math riddle but it's fun!