BrainDen.com - Brain Teasers
• 0

## Question

Determine a cycle of five 4-digit positive integers , each with no leading zero, such that the last 2 digits of each number are equal to the first 2 digits of the next number in the cycle with the proviso that each of the 5 numbers must be exactly one of the following types : Square, Cube, Triangular, Prime, Fibonacci (albeit not necessarily in this order). Each of the five types must be represented exactly once.

Edited by K Sengupta

## Recommended Posts

• 0

(1728,2850,5041,4181,8117) which cycles as (Cube, Triangular, Square, Fibonacci, Prime)

##### Share on other sites
• 0

8649.|.................|.7841

3249.|.4913.1378.|

1849.|.................|.7867

these are the only solutions

If u generate all of this number in a 4 digits range, u will notice that there is a quite small amount of squares (12)

and Fibonaccis (4, and 2 of them are starting with *5 so they cant be the ending of a prime number), but the solution the 12

squares. u have to check the starting and ending numbers of boundaries.

all of this stuff is about 10 minutes, so quicker than writing a program.

Edited by det

##### Share on other sites
• 0

my answer is for the Square, Cube, Triangular, Prime, Fibonacci order

##### Share on other sites
• 0

8649.|.................|.7841

3249.|.4913.1378.|

1849.|.................|.7867

these are the only solutions

If u generate all of this number in a 4 digits range, u will notice that there is a quite small amount of squares (12)

and Fibonaccis (4, and 2 of them are starting with *5 so they cant be the ending of a prime number), but the solution the 12

squares. u have to check the starting and ending numbers of boundaries.

all of this stuff is about 10 minutes, so quicker than writing a program.

I didn't see any Fibonacci number in there nor did I spot a cycle. Please elaborate.

##### Share on other sites
• 0

oh..i forgot the Fibonacci numbers

..S........C........T........P.......F

8649 |...................| 7841 | 4181

3249 | 4913 | 1378 |

1849 |...................| 7867 | 6765

Edited by det

##### Share on other sites
• 0

oh..i forgot the Fibonacci numbers

..S........C........T........P.......F

8649 |...................| 7841 | 4181

3249 | 4913 | 1378 |

1849 |...................| 7867 | 6765

OK, but they don't cycle. The last two digits of the last number (in this case Fibonacci) must be the first two digits of the first number (in this case Square). I'm afraid you don't have any solutions to the OP here.

##### Share on other sites
• 0

ok, cycle.. i was drunk or i dont know, sorry..

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

×