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  • four numbers such that the sum of every two numbers & sum of all four numbers may be perfect square

    Reya

    Reya

    @reya-SMihdC
    Updated: Mar 11, 2011
    Views: 1.4K
    1.Can you find four numbers such that the sum of every two numbers and the sum of all four numbers may be perfect squares???

    2.I have a wooden cube 3 on a side and a buzz saw.The cube can be cut into 27 one inch cubes by the buzz saw.Only 6 cuts of saw are necessary to make 27 one inch cubes keeping the pieces of cubes together.Can you reduce the no of cuts by rearranging the piecess after each cut??If yes, how is it done??If no,why cant it be done??

    3. Find the largest possible number containing any 9 of the 10 digits considering 0 that shud be divisible by 11, without a remainder??

    4.Can you rearrange the position of the numbers 1 to 10 so that the sum of any two adjacent numbers is equal to the sum of the pair of numbers at the opposite ends of the diameters??
    [​IMG]
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Replies

  • PraveenKumar Purushothaman

    Member • Mar 11, 2011

    Answer for the first one.

    Answer for the first one. The four numbers are:
    A. 10430
    B. 3970
    C. 2114
    D. 386

    Explanation:
    A+B = 14400 = 120[SUP]2[/SUP]
    A+C = 12544 = 112[SUP]2[/SUP]
    A+D = 10816 = 104[SUP]2[/SUP]
    B+C = 6084 = 78[SUP]2[/SUP]
    B+D = 4356 = 66[SUP]2[/SUP]
    C+D = 2500 = 50[SUP]2[/SUP]
    A+B+C+D = 16900 = 130[SUP]2[/SUP]

    Hope this is correct! 😀
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  • Reya

    Member • Mar 12, 2011

    You are right 😀
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  • CIVILPRINCESS

    Member • Mar 12, 2011

    3. 987634120?

    test of divisibility : (9+7+3+1+0)-(8+6+4+2)=0
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  • Reya

    Member • Mar 12, 2011

    No,You are wrong 😔
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  • Reya

    Member • Mar 12, 2011

    @Niru:I asked you the largest possible no 😀
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  • silverscorpion

    Member • Mar 13, 2011

    3. Is it 986745320?
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  • Reya

    Member • Mar 13, 2011

    largest number 😀Greater than the value you specified!!Try again 😀
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  • PraveenKumar Purushothaman

    Member • Mar 13, 2011

    silverscorpion
    3. Is it 986745320?
    1 is missing dude and 0 is not supposed to be in the last place.
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  • silverscorpion

    Member • Mar 13, 2011

    praveenscience
    1 is missing dude and 0 is not supposed to be in the last place.
    The question says use any of the 9 digits... so, it's ok to use 0 i guess.. also, if you use 1 and not 0, then you cant make a number divisible by 11.

    If we use digits from 1 to 9, their sum is 45. If we use 2 to 9 and 0, their sum is 44. A number, the sum of whose digits is odd, cannot be divisible by 11.
    So, we have to use 2 to 9 and 0. Using these, I tried to make the biggest number possible, divisible by 11..
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  • Reya

    Member • Mar 13, 2011

    silverscorpion
    The question says use any of the 9 digits... so, it's ok to use 0 i guess.. also, if you use 1 and not 0, then you cant make a number divisible by 11.
    @Ram:Is it so??You can make a number divisible by 11 if you use 1 and not 0.Think 😀

    @praveen: Rightly said!!
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  • harshajd

    Member • Mar 13, 2011

    3) 987654302
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  • Reya

    Member • Mar 13, 2011

    No harsha 😔 See the above comment there is a hidden clue!!
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  • harshajd

    Member • Mar 13, 2011

    978653412 ??
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  • Reya

    Member • Mar 14, 2011

    No try again 😔
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  • harshajd

    Member • Mar 14, 2011

    4) [​IMG]
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  • harshajd

    Member • Mar 14, 2011

    praveena211
    No try again 😔
    the first one is the max i can find.. give the ans
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  • Reya

    Member • Mar 14, 2011

    Read the question again 😀

    Sum of any two adjacent numbers is equal to the sum of the pair of numbers at the opposite ends of the diameters

    Wrong answer.

    Let others try for the second question!
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  • harshajd

    Member • Mar 14, 2011

    praveena211
    Read the question again 😀

    Sum of any two adjacent numbers is equal to the sum of the pair of numbers at the opposite ends of the diameters

    Wrong answer.

    Let others try for the second question!
    where i went wrong in the 4 ans???
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  • Reya

    Member • Mar 14, 2011

    harshajd
    where i went wrong in the 4 ans???
    Sorry your answer is right 😀Go ahead!!
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  • harshajd

    Member • Mar 14, 2011

    3) I don't think its possible to cut 27 pieces as we need a least of 6 cuts to make the center 1" cube
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  • Reya

    Member • Mar 14, 2011

    Right 😀No matter how the pieces are arranged!
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  • harshajd

    Member • Mar 14, 2011

    ans: 987645230
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  • Reya

    Member • Mar 14, 2011

    praveena211
    You can make a number divisible by 11 if you use 1 and not 0.Think 😀
    What does it mean??Your answer does not have zero in it!!
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  • Jos Raj

    Member • Mar 14, 2011

    I think this is the largest number : 987645230
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  • Reya

    Member • Mar 14, 2011

    @Jos:See the above comment 😀
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  • Jos Raj

    Member • Mar 14, 2011

    I dont think, we would arrive at a solution, by having 1 and not 0, as the difference of the sum of the odd numbers and sum of the even numbers will not be zero......

    Waiting on the answer
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  • harshajd

    Member • Mar 14, 2011

    my last try: 987652413
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  • Reya

    Member • Mar 14, 2011

    Awesome 😀😀Congratulations!!Hats off to you😁😁

    You proved you are a
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  • silverscorpion

    Member • Mar 14, 2011

    harshajd
    my last try: 987652413
    Good!!!

    My bad!! I assumed the difference between sum of odd and even numbers should be zero.. Completely forgot it can also be 11 or any multiple of 11..
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  • saurabhsalvi

    Member • Mar 14, 2011

    ans for the FOUTH QUESTION
    the order of numbers is 10,1,4,5,8,9,2,3,6,7....arrange this numbers clockwise....
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  • saurabhsalvi

    Member • Mar 14, 2011

    answer for FOURTH QUESTION
    the order of numbers are...10,1,4,5,8,9,2,3,6,7....arrange the numbers clockwise...
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  • Reya

    Member • Mar 15, 2011

    Answers are already given by CEeans!!Didn't you see that??
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  • Reya

    Member • Mar 17, 2011

    Below there are 9 digits arranged to form four square numbers
    9,81,324,576
    How would you put them together so that they form a single smallest possible square number and a single largest possible square number??
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  • harshajd

    Member • Mar 18, 2011

    praveena211
    Below there are 9 digits arranged to form four square numbers
    9,81,324,576
    How would you put them together so that they form a single smallest possible square number and a single largest possible square number??
    does this mean, have to use all 9 digits(any arrangement) and find smallest and largest square no??
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  • Reya

    Member • Mar 22, 2011

    Yes,it should use all the nine digits of any arrangement to find the smallest and largest!!
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  • harshajd

    Member • Mar 23, 2011

    smallest number 139854276 (11826 x 11826)
    largest number 923187456 (30384 x 30384)
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  • Reya

    Member • Mar 23, 2011

    Correct!! I should go for difficult questions i guess😉
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  • harshajd

    Member • Mar 23, 2011

    yeah please.... but bring it on with lot of equations (i am weak in there ) 😉
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  • Gitesh kumar

    Member • Dec 12, 2016

    Praveen-Kumar
    Answer for the first one.

    Answer for the first one. The four numbers are:
    A. 10430
    B. 3970
    C. 2114
    D. 386

    Explanation:
    A+B = 14400 = 120[SUP]2[/SUP]
    A+C = 12544 = 112[SUP]2[/SUP]
    A+D = 10816 = 104[SUP]2[/SUP]
    B+C = 6084 = 78[SUP]2[/SUP]
    B+D = 4356 = 66[SUP]2[/SUP]
    C+D = 2500 = 50[SUP]2[/SUP]
    A+B+C+D = 16900 = 130[SUP]2[/SUP]

    Hope this is correct! 😀
    Can you show me step by step solution how this has been solved.
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