perplexus.info :: Just Math : Ambiguous dice

Ambiguous dice (Posted on 2010-12-21)

A set of five dice is marked 1 to 6, but instead of commonly used spots bears Arabic digits .
After a single roll of dice they are arranged to represent a 5-digit number.
It is found that this number fullfils ALL of the following conditions:
1. There is no descending order of digits within this number.
2. No digit is repeated more than twice within this number.
3. At least one of the digits in the number is bigger than 5.

How many such 5 - digit numbers exist?

No Solution Yet Submitted by Ady TZIDON

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

re(2): computer findings--now adding the ambiguity

Comment 3 of 3 |

(In reply to re: computer findings--unambiguously by Ady TZIDON)

All those sets with 9 as the highest value are shown:

5 6 6 9 9
4 6 6 9 9
3 6 6 9 9
2 6 6 9 9
1 6 6 9 9
5 5 6 9 9
4 5 6 9 9
3 5 6 9 9
2 5 6 9 9
1 5 6 9 9
4 4 6 9 9
3 4 6 9 9
2 4 6 9 9
1 4 6 9 9
3 3 6 9 9
2 3 6 9 9
1 3 6 9 9
2 2 6 9 9
1 2 6 9 9
1 1 6 9 9
4 5 5 9 9
3 5 5 9 9
2 5 5 9 9
1 5 5 9 9
4 4 5 9 9
3 4 5 9 9
2 4 5 9 9
1 4 5 9 9
3 3 5 9 9
2 3 5 9 9
1 3 5 9 9
2 2 5 9 9
1 2 5 9 9
1 1 5 9 9
3 4 4 9 9
2 4 4 9 9
1 4 4 9 9
3 3 4 9 9
2 3 4 9 9
1 3 4 9 9
2 2 4 9 9
1 2 4 9 9
1 1 4 9 9
2 3 3 9 9
1 3 3 9 9
2 2 3 9 9
1 2 3 9 9
1 1 3 9 9
1 2 2 9 9
1 1 2 9 9
5 5 6 6 9
4 5 6 6 9
3 5 6 6 9
2 5 6 6 9
1 5 6 6 9
4 4 6 6 9
3 4 6 6 9
2 4 6 6 9
1 4 6 6 9
3 3 6 6 9
2 3 6 6 9
1 3 6 6 9
2 2 6 6 9
1 2 6 6 9
1 1 6 6 9
4 5 5 6 9
3 5 5 6 9
2 5 5 6 9
1 5 5 6 9
4 4 5 6 9
3 4 5 6 9
2 4 5 6 9
1 4 5 6 9
3 3 5 6 9
2 3 5 6 9
1 3 5 6 9
2 2 5 6 9
1 2 5 6 9
1 1 5 6 9
3 4 4 6 9
2 4 4 6 9
1 4 4 6 9
3 3 4 6 9
2 3 4 6 9
1 3 4 6 9
2 2 4 6 9
1 2 4 6 9
1 1 4 6 9
2 3 3 6 9
1 3 3 6 9
2 2 3 6 9
1 2 3 6 9
1 1 3 6 9
1 2 2 6 9
1 1 2 6 9
4 4 5 5 9
3 4 5 5 9
2 4 5 5 9
1 4 5 5 9
3 3 5 5 9
2 3 5 5 9
1 3 5 5 9
2 2 5 5 9
1 2 5 5 9
1 1 5 5 9
3 4 4 5 9
2 4 4 5 9
1 4 4 5 9
3 3 4 5 9
2 3 4 5 9
1 3 4 5 9
2 2 4 5 9
1 2 4 5 9
1 1 4 5 9
2 3 3 5 9
1 3 3 5 9
2 2 3 5 9
1 2 3 5 9
1 1 3 5 9
1 2 2 5 9
1 1 2 5 9
3 3 4 4 9
2 3 4 4 9
1 3 4 4 9
2 2 4 4 9
1 2 4 4 9
1 1 4 4 9
2 3 3 4 9
1 3 3 4 9
2 2 3 4 9
1 2 3 4 9
1 1 3 4 9
1 2 2 4 9
1 1 2 4 9
2 2 3 3 9
1 2 3 3 9
1 1 3 3 9
1 2 2 3 9
1 1 2 3 9
1 1 2 2 9

There are 140 of these.

Added to the 75 previously found, where the largest value was 6, this makes 215 possible 5-digit numbers.

The new ones were found with:

CLS
d5 = 9
nct(d5) = nct(d5) + 1
FOR d4 = d5 TO 1 STEP -1
IF nct(d4) < 2 AND (d4 = 9 OR d4 <= 6) THEN
    nct(d4) = nct(d4) + 1
FOR d3 = d4 TO 1 STEP -1
IF nct(d3) < 2 AND (d3 = 9 OR d3 <= 6) THEN
    nct(d3) = nct(d3) + 1
FOR d2 = d3 TO 1 STEP -1
IF nct(d2) < 2 THEN
    nct(d2) = nct(d2) + 1
FOR d1 = d2 TO 1 STEP -1
IF nct(d1) < 2 THEN
    nct(d1) = nct(d1) + 1
    PRINT d1; d2; d3; d4; d5
    numCt = numCt + 1
    IF numCt MOD 40 = 0 THEN
     DO: LOOP UNTIL INKEY$ > ""
     PRINT
    END IF
    nct(d1) = nct(d1) - 1
END IF
NEXT
    nct(d2) = nct(d2) - 1
END IF
NEXT
    nct(d3) = nct(d3) - 1
END IF
NEXT
    nct(d4) = nct(d4) - 1
END IF
NEXT
PRINT numCt

Posted by Charlie on 2010-12-23 03:33:13

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info