four numbers such that the sum of every two numbers & sum of all four numbers may be perfect square
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]](proxy.php?image=http%3A%2F%2Fi54.tinypic.com%2Foaowf6.png&hash=97707aa23f1ee2e1d05403704ef7f631)
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??
Replies
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PraveenKumar PurushothamanAnswer 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! 😀 -
ReyaYou are right 😀
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CIVILPRINCESS3. 987634120?
test of divisibility : (9+7+3+1+0)-(8+6+4+2)=0 -
ReyaNo,You are wrong 😔
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Reya@Niru:I asked you the largest possible no 😀
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silverscorpion3. Is it 986745320?
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Reyalargest number 😀Greater than the value you specified!!Try again 😀
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PraveenKumar Purushothaman
1 is missing dude and 0 is not supposed to be in the last place.silverscorpion3. Is it 986745320? -
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.praveenscience1 is missing dude and 0 is not supposed to be in the last place.
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.. -
Reya
@Ram:Is it so??You can make a number divisible by 11 if you use 1 and not 0.Think 😀silverscorpionThe 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.
@praveen: Rightly said!! -
harshajd3) 987654302
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ReyaNo harsha 😔 See the above comment there is a hidden clue!!
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harshajd978653412 ??
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ReyaNo try again 😔
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harshajd4)
![[IMG]](proxy.php?image=http%3A%2F%2Fimg.drlinky.com%2Fimages%2F6564%2Fqn4.PNG&hash=1eae5619d457efadbf8e6b47f82068e5)
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harshajd
the first one is the max i can find.. give the anspraveena211No try again 😔 -
ReyaRead 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! -
harshajd
where i went wrong in the 4 ans???praveena211Read 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! -
Reya
Sorry your answer is right 😀Go ahead!!harshajdwhere i went wrong in the 4 ans??? -
harshajd3) 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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ReyaRight 😀No matter how the pieces are arranged!
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harshajdans: 987645230
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Reya
What does it mean??Your answer does not have zero in it!!praveena211You can make a number divisible by 11 if you use 1 and not 0.Think 😀 -
Jos RajI think this is the largest number : 987645230
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Reya@Jos:See the above comment 😀
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Jos RajI 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 -
harshajdmy last try: 987652413
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ReyaAwesome 😀😀Congratulations!!Hats off to you😁😁
You proved you are a -
silverscorpion
Good!!!harshajdmy last try: 987652413
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.. -
saurabhsalvians for the FOUTH QUESTION
the order of numbers is 10,1,4,5,8,9,2,3,6,7....arrange this numbers clockwise.... -
saurabhsalvianswer for FOURTH QUESTION
the order of numbers are...10,1,4,5,8,9,2,3,6,7....arrange the numbers clockwise... -
ReyaAnswers are already given by CEeans!!Didn't you see that??
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ReyaBelow 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?? -
harshajd
does this mean, have to use all 9 digits(any arrangement) and find smallest and largest square no??praveena211Below 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?? -
ReyaYes,it should use all the nine digits of any arrangement to find the smallest and largest!!
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harshajdsmallest number 139854276 (11826 x 11826)
largest number 923187456 (30384 x 30384) -
ReyaCorrect!! I should go for difficult questions i guess😉
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harshajdyeah please.... but bring it on with lot of equations (i am weak in there ) 😉
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Gitesh kumar
Can you show me step by step solution how this has been solved.Praveen-KumarAnswer 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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