how many such??

Number Theory Level 3

from 100 to 500 how many numbers are such that the sum of the cubes of the digits of the number is the number itself.??


The answer is 4.

Pradeep Ch by Pradeep Ch , 23, India

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4 solutions

Abhishek Ghosh
Mar 20, 2014

This are known as Armstrong Numbers AND THE NUMBERS ARE 153, 370, 371, 407

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Exactly.

Krishna Ar - 7 years, 2 months ago

right they didn't mentioned in the question

Saurav Sharma - 7 years ago

.

rachit parikh - 7 years, 2 months ago
Pradeep Ch
Mar 12, 2014

the numbers are 153, 370, 371, 407.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

excel was good helper for it

dina maulina - 7 years, 3 months ago

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lol!

Pradeep Ch - 7 years, 3 months ago
Masbahul Islam
Apr 27, 2014

VBA code:

s = 0

For a = 1 To 4

For b = 0 To 9

For c = 0 To 9

If a ^ 3 + b ^ 3 + c ^ 3 = Int(a & b & c) Then

s = s + 1

End If

Next c, b, a

MsgBox (s)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

hey can you do a c++ program to find these no in programmming

Saurav Sharma - 7 years ago
Dean Clidoro
Mar 13, 2014

Solution:

  1. write down all the sum of number starting from 7 then other number

  2. we will find that there are 3 number that has the same sum as there digits cube

  3. assume 1 percent probability or assume a chance of having another number with the sum of its digits cube is equal to itself is 1

  4. then there are all in all 4 numbers.....check

0 Helpful 0 Interesting 0 Brilliant 0 Confused

yea actually this is how you solve it... if u want a number between 100 nd 500... cube of 6 = 216 nd 7 = 343 so 7 is very much likely to be in the number... :)

Pradeep Ch - 7 years, 3 months ago

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