Think about it

wolfgang59

Quiz Master

Posers and Puzzles

30 Dec 13

wolfgang59

Quiz Master

RHP Arms

Joined: 09 Jun 07
Moves: 48794

30 Dec 13

1 = 5
2 = 505
3 = 5005
4 = 50005
5 =

?

coquette

Already mated

Omaha, Nebraska, USA

Joined: 04 Jul 06
Moves: 1118476

30 Dec 13

Originally posted by wolfgang59
1 = 5
2 = 505
3 = 5005
4 = 50005
5 =

?

5 = 1

as 1 = 5

iamatiger

Joined: 26 Apr 03
Moves: 26771

02 Jan 14

the digits of each number can be rearranged to give n other valid numbers (i.e. without leading zeros)

e.g.
505, 550
5005,550,5050

wolfgang59

Quiz Master

RHP Arms

Joined: 09 Jun 07
Moves: 48794

02 Jan 14

Originally posted by coquette
5 = 1

as 1 = 5

correct

iamatiger

Joined: 26 Apr 03
Moves: 26771

03 Jan 14

Originally posted by wolfgang59
1 = 5
2 = 505
3 = 5005
4 = 50005
5 =

?

but, it is ambiguous:

1 = 5 which has 1 possible arrangement (5)
2 = 505 which has exactly 2 possible arrangements (505, 550)
3 = 5005 : 3 arrangements (5005, 5050, 5500)
4 = 50005: 4 arrangements (50005, 50050, 50500, 55000)

so the fomula could be:
for any number n, the lowest number, made of only the digits 0 and 5, which can be rearranged into n distinct legal numbers.

so
5 = 500005

Sebastian Yap

Joined: 07 Jul 12
Moves: 2114

03 Jan 14

Your solution is not unique. 55000, 50500, 50050 also fits your requirements.

iamatiger

Joined: 26 Apr 03
Moves: 26771

04 Jan 14

1 edit

Originally posted by Sebastian Yap
Your solution is not unique. 55000, 50500, 50050 also fits your requirements.

As I said:

for any number n, the lowest number, made of only the digits 0 and 5, which can be rearranged into n distinct legal numbers, i.e. 50005. This also fits the given numbers.

talzamir

Art, not a Toil

60.13N / 25.01E

Joined: 19 Sep 11
Moves: 58046

18 Jan 14

f(n) = 5 + 5 x 10^n would be good for most cases but not f(1).. oh well.

"lowest POSITIVE number.." and Tiger's wording is even more flawless, eliminating negative numbers and 1 = 0.

iamatiger

Joined: 26 Apr 03
Moves: 26771

20 Jan 14

Originally posted by talzamir
f(n) = 5 + 5 x 10^n would be good for most cases but not f(1).. oh well.

"lowest POSITIVE number.." and Tiger's wording is even more flawless, eliminating negative numbers and 1 = 0.

Good point talz!