17 replies to this topic

[ALFRED]

Cipher - Back to the Number Puzzles
Find the cipher if:

1. The cipher is made of 6 different numerals.
2. Even and odd figures alternate, including zero (in this case as an even number).
3. The difference of adjacent numerals is always bigger than one.
4. The first two numerals (as one number) as well as the two middle numerals (as one number) are a multiple of the last two numerals (as one number).

What is the cipher? (more than 1 solution)

Spoiler for Solution

Cipher - solution
The possible 2 last numerals are as follows: 03, 05, 07, 09, 14, 16, 18, 25, 27, 29 and 30. At least two multiples less than 100 (this condition is already accomplished), which consist of even and odd numeral (respecting all other conditions) are for 03, 07, 09 and 18 as follows:
03 – 27, 63, 69, 81
07 – 49, 63
09 – 27, 63, 81
18 – 36, 72, 90
There are 5 numbers that can be made of these pairs of numerals to create the cipher: 692703, 816903, 496307, 816309 and 903618. (If we assume, that also in the number 903618 is accomplished the requirement to alternate even and odd numbers, despite the opposite order.)

I'm not seeing how the first two and second two numerals are a multiple of the last two numerals in 496307. Can you help me out?

[ALFRED]

I'm not seeing how the first two and second two numerals are a multiple of the last two numerals in 496307. Can you help me out?

nevermind I see it now. I thought you meant the sum of the two numerals. which surprisingly works for all the other solutions.

[gmarsha11]

What about 270903?

EDIT: ...wait... That doesn't meet the 1st requirement that they be "different" numerals.

so, 274503 should meet the requirements.

2nd EDIT: Crap. the 4 and 5 are consecutive. hmmm....

Edited by gmarsha11, 26 March 2008 - 10:20 PM.

[demented]

692703 is what I've come up with.

Not that my entry does it, but the OP could've made it more interesting if he asked for the 'smallest' possible number meeting the criteria.

Edited by demented, 12 April 2008 - 08:13 AM.

[altocumulus]

I got 276309 by trial & error, I'm sure there are more.



"adjacent" means next to, not the 1st and 6th digit of the final number.

276309 has 7 & 6 next to each other, and also the questioner doesn't state whether the numerals 9 & 0 should be regarded as adjacent (as they are on a bicycle padlock for example)

[altocumulus]

Well I think there are only two possible solutions, if 9 and 0 are to be regarded as adjacent and therefore excluded.

692703 and 496307

these others use 9 & 0 together:

903618; 816903 and 816309

[Polynym]

Am I correct in assuming

Spoiler for assumption

there are exactly 65 missed a couple adjacent possible soutions?
or

Spoiler for maybe

2 if 0 and 9 are considered adjacent

Edited

Edited by Polynym, 05 August 2010 - 02:01 PM.

[Brain Tickler]

thank you to everyone for using a spoiler..much obliged

Edited by Brain Tickler, 03 September 2010 - 01:46 PM.