Debasis
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Posts posted by Debasis
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1 2 3 4 5 6 7 8 9
Arrange these numbers into two separate groups so that they add up to same total.
Note : you cant turn 9 upside down and make it 6
You have to turn the 9 into a six.
Numbers 1-9 total 45, which can't be evenly split.
Making the 9 a 6 reduces that total by 3 to 42.
So we need two groups that each total 21.
1 2 3 4 5 6 and 6 7 8 should do it.
Or turn the 6 into 9, increasing the total by 3 to 48.
1 2 3 4 5 9 and 7 8 9 do it for that case.
this is what even i think how can you split 45 into two equal parts...P.S- he noted that we cant use 9 as 6...
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i think that there is something wrong with the question....we can see that the total from 1 to 10 is 45 how can you divide 45 into two equal parts.....is there some cheating involved??i have got this -
18365 / 9274 they add up to 23 and 22...let me see what else i can do -
i think it is O because even if we invert the page the letter will change but o remains the same...
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... this triangle is equilateral.(If my drawing was correct.)
Correct. Good job.
I wonder if there is a proof of this that is not overly complex?
Edit:
Well, No. I just found the proof, and it's not beautiful for its simplicity.
You start with the Law of Sines, and 2 1/2 pages later you have a symmetrical expression for one side.
"Do not try this at home."
oh i am so sorry .....i mistook it for the eulers line....my bad...
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complete the following series ...it is a bit harder than the previous ones...
11, 12, 13, 14, 15, 16, 17, 20, 22, 24, ? , 100, 121, ?
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use spoiler !!the little button in the post box that says "s"!!
61 !
The nos. are squares from 9 to 4, but inverted.I mean,
92 = 81
82 =64
72 =49
62 =36
52 =25
These nos. have been written backwards to form the series.So next term would be 61 as 42 =16, and it gives 61 when written backwards!
use spoiler !!the little button in the post box that says "s"!!
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use spoiler!
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228^251 * 126^23416 * 37^217 * 213^19. what will be the last digit of the resulting Answer?
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Two consecutive numbers are given to A and B. when A is asked ‘do you know B’s number?’ A denies. when B is asked whether he knows A’s no., B also denies. at the very moment, A replies that he knows B’s number. what may be B’s number?
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Which term will be the next term in the series?
18, 46, 94, 63, 52, ?
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Did you mean edges or faces?
even i am having the same confusion...
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the hexagonal pencil will 18 sides (or 18 edges) if you are talking about faces then it will have eight faces ....however when it is sharpened the results are different...
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Suppose n tickets numbered 1-n are in a box, and you draw one of them
You don't know how many tickets are in the box, but you are asked to estimate how many there are.
Your ticket has the number p on it.
What estimate of n has the highest likelihood of being correct?
It seems like this problem is dependent upon what is a reasonable a priori distribution for N.
Let P(N) be the prior distribution for the number N. Let P(p|N) be the conditional probability for p given N; we know that P(p|N) = 1/N. We wish to compute the conditional probability P(N|p), which can be expanded using Bayes theorem
So, if we are given a well-defined probability function P(N), we can easily compute the number N that gives that maximum probability P(N|p).
The problem is that we are not given what P(N) is. One reasonable choice would be to assume that P(N) is the improper uniform distribution from p to infinity (every number has an equal chance of occuring). However, if we plug that improper distribution into the equation above, we would be able to cancel out P(N), but we'd end up with a harmonic series in the denominator, which does not converge.
OMG!you are one hell of a methematician...lol
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1800 ft.
why?
Call the width of the river
w. Then from the moment the boats began moving to the moment the boats crossed for the first time, boat "A" traveled 700 feet and boat "B" traveled (w - 700) feet. Since they completed their respective distances in the same amount of time, and each boat is traveling with a constant speed (say Va for boat "A" and Vb for boat "B"), we have that 700 / Va = (w - 700) / Vb. By similar reasoning, from the moment the boats first crossed to the moment they crossed a second time, boat "A" completed a distance of (w - 700) + 300, while boat "B" completed a distance of 700 + (w - 300), and so we have that (w - 400) / Va = (w + 400) / Vb.Dividing one equation by the other cancels out the terms Va and Vb, leaving: 700 / (w - 400) = (w - 700) / (w + 400). With a few algebraic manipulations, this simplifies to w*(w - 1800) = 0, from which the answer is apparent.
Thanks!
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the other person is running towards the frst person at 20m/s thus relative speed is 10+20 m/s or 30 m/s
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Do we have to name that point?
if we have to name then the angle bisectors of a triangle meet at the incentre (i learned about it in school) and i dont know about the point where trisection meet.....i do hope you want us to find coordinates of the point...
You're right about the bisector case.
But for the trisector case there is more than one point.
In fact there are three places where a trisector of one angle first intersects a trisector of one of the other angles.
And there is something special about those three points.
the three point where the trisectors meet lie on the same line...
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9/9
9did you mean (9/9)^9 if it is then it is correct...There are many possible combinations...i wanted the one with subtraction sign...
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Use three 9's and arrange them using the mathematical signs to form the number one.
There is a subtraction sign.
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1
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1
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didnt your first image touch only one coin.??/
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Do we have to name that point?
if we have to name then the angle bisectors of a triangle meet at the incentre (i learned about it in school) and i dont know about the point where trisection meet.....i do hope you want us to find coordinates of the point...
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Product of the ages is 36. So if you look at the factors of 36 only two combinations are such whose sum is equal i.e. 9,2,2 and 6,6,1 (one mentioned that sum of the ages coincides with the number of the house across the street) and this made it unsolvable at this point. Now given that the oldest daughter has beautiful blue eyes or simply that the oldest daughter exists, the answer is 9,2,2.
what about 2,3 and 6??
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it should be the 4 th dice (with five) here the explanation:most of the intuitive people will take the dice with 6 but we can see that the probability that 6 will come is 1/3 .....but in the 5 nubered dice there is a 1/2 cahnce that you will get 5.....extend this to all dices and you will get the answer...
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...and sqrt(37) is the correct distance between the towns. For any
a and b, where a is the distance from the car to Alpha and b is the distance from the car to Beta, the maximum distance from the car to Gamma is a+b and is achieved when the angle formed by the lines connecting the car with Alpha and Beta is equal 120 degrees. Applying the law of cosines with 120 degree angle we get the distance between towns = sqrt( 32 + 42 - 2 * 3 * 4 * cos(pi/3) ) = sqrt(37).hey man can you tell me how you worked out that the angle between alpha and beta should be 120 degrees .i just acant understand..Thanks
I knew someone would ask that question
It was a little messy and maybe not in the most efficient way, but...
I used the laws of cosines and sines to express the distance to Gamma as a function of the angle between Alpha and Beta. Then I to took a derivative of that function to find the local maxima and found it to be at 120 degrees. If I have more time later, I may post the complete solution
thanks!
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1800 ft.
why?
Number game 2
in New Logic/Math Puzzles
Posted