Math Is Fun Forum

Lillyani

Guest

5 digit number puzzle

please help me with this problem

math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

Re: 5 digit number puzzle

What's the puzzle you need help with?

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phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,818

Re: 5 digit number puzzle

Hi Lillyani,

Welcome to the forum!

I guess you're referring to the puzzle found here:

What 5-digit number has the following features:

If we put the numeral 1 at the beginning, we get a number three times smaller than if we put the numeral 1 at the end of the number.

The answer and the solution method (algebraic) are given here.

Here's another approach, one that doesn't use an algebraic equation:

Let the 5-digit number be abcde, where each letter represents one of the 5 digits.
From this, the number beginning with 1 is 1abcde, and the number ending with 1 is abcde1.
Note: The fact that the number's letters are different from each other doesn't necessarily mean that the digits are all different.

Work backwards, digit by digit, to find which digit values result in the following:

1abcde
      x3
--------
abcde1
=====

Start by asking this question to find e in 1abcde (and hence in abcde1):
     The product of which digit when multiplied by 3 ends in 1?
     Answer: 7 (ie, 7x3=21)...so e=7 (carry 2...ie, the product's tens unit)

To find d, c, b and a, ask the same question as for e, but this time there's a 'carry' to add. eg, to find d:
     The product of which digit when multiplied by 3, plus the carry 2, ends in 7?
     Answer: 5 (ie, (5x3)+2=17)...so d=5 (carry 1)

So far we have this partial solution:

1abc57
      x3
--------
abc571
=====

...and the rest I'll leave for you to solve.

Last edited by phrontister (2015-05-20 14:00:29)

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