The eight-digit number 23421314 has two 1's, two 2's, two 3's, and two 4's. The two 1's are separated by one digit, the two 2's are separated by two digits, the two 3's are separated by three digits, and the two 4's are separated by four digits.

Now imagine a 14-digit number that contains two 1's, two 2's, two 3's, two 4's, two 5's, two 6's, and two 7's, such that the 1's are separated by one digit, the 2's are separated by two digits, and so on, up to the 7's being separated by seven digits. Actually, there are 52 such numbers; can you find the highest and lowest of them?

 

Solution to the Problem:

The lowest number is 14156742352637 and
the highest is 74151643752362.

Tom Dressen sent in the following program to solve the problem:


def search(num, digit):
    for i in range(len(num)-digit-1):
        if num[i] == 0 and num[i+digit+1] == 0:
            num[i] = num[i+digit+1] = digit
            if digit*2 == len(num):
                print num
            else:
                search(num, digit+1)
            num[i] = num[i+digit+1] = 0

search([0]*14, 1)
James Alarie and Richard Johnson sent in all 52 numbers: 
  
01: 14156742352637
02: 14167345236275
03: 15146735423627
04: 15163745326427
05: 15167245236473
06: 15173465324726
07: 16135743625427
08: 16172452634753
09: 17125623475364
10: 17126425374635
11: 23627345161475
12: 23726351417654
13: 24723645317165
14: 25623745361417
15: 26325734615147
16: 26327435614175
17: 26721514637543
18: 27423564371516
19: 34573641512762
20: 34673245261715
21: 35723625417164
22: 35743625427161
23: 36713145627425
24: 37463254276151
25: 41617435263275
26: 41716425327635
27: 45671415362732
28: 46171435623725
29: 46171452632753
30: 46357432652171
31: 51716254237643
32: 52462754316137
33: 52472654131763
34: 52642753461317
35: 52732653417164
36: 53647352462171
37: 53672352461714
38: 56171354632742
39: 57141653472362
40: 57236253471614
41: 57263254376141
42: 57416154372632
43: 61517346532472
44: 62742356437151
45: 71316435724625
46: 71416354732652
47: 72452634753161
48: 72462354736151
49: 72632453764151
50: 73161345726425
51: 73625324765141
52: 74151643752362


Correctly solved by:

1. James Alarie University of Michigan -- Flint
Flint, Michigan
2. Kristofer Friman Mullhyttan, Sweden
3. Richard Johnson LaJolla, California
4. Akash Patel Columbus, Georgia
5. John Beasley Winchester, Virginia
6. John Funk Ventura, California
7. Viktor Bergqvist Tullängsskolan, Sweden
8. Nina Karlsson Tullängsskolan, Örebro, Sweden
9. Jeffrey Gaither Winchester, Virginia
10. Tom Dressen ---------
11. Britney Ford Winchester, Virginia
12. Ashleigh Rogers Winchester, Virginia
13. Laura LaRusso Winchester, Virginia
14. Patrick Wingfield Winchester, Virginia
15. Jason Storer Winchester, Virginia
16. Misty Carlisle Winchester, Virginia
17. David Wong Winchester, Virginia
18. Brad Stillwagon Winchester, Virginia
19. Victor Karlsson Tullängskolan, örebro, Sweden
20. Chris McCormick Winchester, Virginia
21. Andrew Oliver Winchester, Virginia
22. Nate Wilson Winchester, Virginia