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navik [9.2K]
2 years ago
11

Find out the secret number! Here's the clues

Mathematics
2 answers:
astra-53 [7]2 years ago
8 0

THIS MORON IS WASTING MY POINTS

Aleks04 [339]2 years ago
6 0

Answer:

Step-by-step explanation:

Known facts:

  • multiple of three, five, and seven
  • No digit occurs more than once
  • digit in the tens place is a square number.
  • the digit in the hundreds place is a cube
  • The digit in the hundred thousand places is both a square and a cube.
  • Only the digit in the hundreds place is larger than the digit in the ones place

Analyzing our choices:

  • since the tens place is a square, but cannot be larger than the ones place, it has to be either 1 or 4
  • the hundreds place is a cube which can be 8 not one since the digit in the hundred thousand places is both a square and a cube which is 1
  • also, the number is divisible by 5 meaning that the last digit must be 5 or zero. However, only the hundreds place is larger than the digit in the ones place so it must be 5

Looking at what we have so far:

1 _ _ 8 4 5

  • this number is divisible by 3 and cannot be larger than 5 which is in the units place
  • when a number is divisible by 3 all its digits must add to a number that is divisible by 3, meaning that the last unfilled digits can be filled by '0' and '3'
  • now the order of '0' and '3' is determined by whether the number is divisible by 7

Result:  103845 is the secret number

Hope that helps!

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