Go back
Think about it

Think about it

Posers and Puzzles

Clock
Vote Up
Vote Down

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

?

Clock
Vote Up
Vote Down

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

?
5 = 1

as 1 = 5

Clock
Vote Up
Vote Down

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

Clock
Vote Up
Vote Down

Originally posted by coquette
5 = 1

as 1 = 5
correct

Clock
Vote Up
Vote Down

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

Clock
Vote Up
Vote Down

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

Clock
1 edit
Vote Up
Vote Down

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.

Clock
Vote Up
Vote Down

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.

Clock
Vote Up
Vote Down

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!

Cookies help us deliver our Services. By using our Services or clicking I agree, you agree to our use of cookies. Learn More.