## See if you can follow this…

Posted by Karl Sharman on November 12, 2010 – 8:58 am

What is the 5-digit number in which the sum of the first two digits is one smaller than the third, the third is double the fourth, the fourth is double the last, the third is the product of the fourth and fifth, the second is five more than the first, and the first is one-eighth the third and also one-fourth of the fourth?

November 12th, 2010 at 9:53 am

16842

If the third is double the fourth, and the fourth is double the fifth, then there are only 2 combinations of the last 3 digits that would fit that solution (_ _ 8-4-2 or _ _ 4-2-1).

If the third is the product of the fourth and fifth then _ _ 4-2-1 doesn’t work so the last digits are 8-4-2.

The first is 1/8 the third and 1/4 the fourth so must be 1

The second is five more than the first so must be 6.

As a check we also know that the sum of the first two is one less than the third (1+6 = 8-1)

November 12th, 2010 at 9:54 am

i came up with 7 equations for 5 unknowns…

lets say the 5-digit number is represented by ‘abcde’

a + b = c – 1

c = 2 * d

d = 2 * e

c = d * e

b = a + 5

a = 1/8 * c

a = 1/4 * d

a = 1; b = 6; c = 8; d = 4; e = 2

16842

November 12th, 2010 at 9:58 am

Well done Dual Aspect. beat me by 1 minute.

November 12th, 2010 at 1:09 pm

16842….

November 14th, 2010 at 4:05 am

i did it somehow but the answer was the same like all the others..16842 …but very tricky .:P

November 14th, 2010 at 9:20 am

11248

November 15th, 2010 at 12:35 pm

16842

i did exactly the same like DP..

November 15th, 2010 at 5:17 pm

The first 5 statements can be written as:

(1) a + b – c = -1

(2) c – 2d = 0

(3) d – 2e = 0

(4) a – b = -5

(5) 8a – c = 0

The sixth statement is redundant.

(1)+(4) => (6) 2a – c = -6

(5)-4(6) => 3c = 24 => (7) c = 8

(7)-(2) => 2d = 8 => (8) d = 4

(7)+(5) => (9) a = 1

(9)-(4) => (10) b = 6

(8)-(3) => (11) e = 2

So abcde = 16842

November 15th, 2010 at 5:20 pm

You can solve simultaneous equations on wolframalpha:

http://www.wolframalpha.com/input/?i=a%2Bb%2B1%3Dc%2Cc%3D2d%2Cd%3D2e%2Cb%3Da%2B5%2C8a%3Dc dow it for this problem.

November 15th, 2010 at 10:58 pm

16842

November 16th, 2010 at 8:38 am

I came up with 16842. Looks like many others did too. I didn’t use any math, just followed the rules in the order that I used them:

“The 3rd is double the 4th” and “The 4th is double the 5th”

Possibilities:

xx421

xx842

“The first 2 digits is one smaller than the 3rd”

Possibilities:

12421

21421

30421

34842

43842

52842

25842

16842

61842

70842

“The 3rd is the product of the fourth”, which knocks out the xx421 numbers.

Possibilities:

34842

43842

52842

25842

16842

61842

70842

“The 2nd is five more than the first”. This is narrows it down to:

16842

“The first is one-eight the third and also one-fourth the fourth”. this just confirms that it still works with 16842.

November 16th, 2010 at 11:32 am

16842

Far too much information was provided.

What is the 5-digit number in which the sum of the first two digits is one smaller than the third, the third is double the fourth, the fourth is double the last, and the first is one-eighth the third and also one-fourth of the fourth?

These are not needed. the third is the product of the fourth and fifth, the second is five more than the first

November 16th, 2010 at 7:21 pm

16842

five more than the first made this easy

The first is one-eight the third and also one-fourth the four just confirmed it

November 17th, 2010 at 7:49 am

16842

i did the way hw gaurav did!

its correct 1+6=8-1

8=4×2

1/8×8=1 nd 1/4×4=1