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An “Armstrong number” is an n-digit number that is equal to
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17 Apr 2020, 10:52
17 Apr 2020, 10:52
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An “Armstrong number” is an n-digit number that is equal to the sum of the nth powers of its individual digits. For example, 153 is an Armstrong number because it has 3 digits and 1^3 + 5^3 + 3^3 = 153. What is the digit k in the Armstrong number 1,6k4 ?
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3
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Re: An “Armstrong number” is an n-digit number that is equal to
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17 Apr 2020, 11:03
17 Apr 2020, 11:03
1
Carcass wrote:
An “Armstrong number” is an n-digit number that is equal to the sum of the nth powers of its individual digits. For example, 153 is an Armstrong number because it has 3 digits and 1^3 + 5^3 + 3^3 = 153. What is the digit k in the Armstrong number 1,6k4 ?
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3
1,6k4 is a 4-digit number.
So, 1⁴ + 6⁴ + k⁴ + 4⁴ = 16k4
Evaluate: 1 + 1296 + k⁴ + 256 = 16k4
Simplify: 1553 + k⁴ = 16k4
Whatever k is, it must be the case that the UNITS digit of k⁴ is 1, so that 1553 + k⁴ = 16k4
Test some values..
k = 1: 1⁴ = 1, so we get: 1553 + 1 = 1554 NO GOOD
k = 3: 3⁴ = 81, so we get: 1553 + 81 = 1634 WORKS!!
Answer: 3
Cheers,
Brent
gmatclubot
Re: An “Armstrong number” is an n-digit number that is equal to [#permalink]
17 Apr 2020, 11:03
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