Find a number such that when you move the first digit to the last place, the new number is 1.5 times the original number.( i.e. if original number is 1234, the new number is 2341. Note, the answer is not necessarily 4 digits long).
(Hint: You will be surprised by the answer if you do find it. You would be even more surprised it only requires some simple maths to work out.)
2007-03-09 14:08:16 · 18 answers · asked by Anonymous in Entertainment & Music ➔ Jokes & Riddles
After some thought as to the answer, this is what I came up with:
- Let an, a3, a2, a1, a0 = numbers of X
-- start out with X = a0 + 10a1 + 100a2 + 10^n*an
Move the first digit to last place:
an + 10a0 + 100a1 + 1000a2 .. + 10^n*a(n-1)
= 1.5(a0 + 10a1 + 100a2 .. + 10^n*an)
----8.5[a0 + 10a1 + 100a2 ... + 10^(n-1)*a(n-1)] = (1.5*10^n - 1)an
---- 8.5(x - 10^n*an) = (1.5*10^n - 1)an
---- x = (1.5*10^n - 1)an / 8.5 + 10^n*an
-need_ 2(1.5*10^n - 1) = (3*10^n -2) to be a multiple of 17.
--- 3*10^n = 2 [mod 17]
----[mod 17]
The value of 10^n [mod 17] cycles through the values 1 to 16, reaching 12 at n = 15, 31, 47, 63, etc. (1111111111111111) can be divided by 17.
Smallest solut. will have 16 digits:
formula for x:
x = (1.5*10^n - 1)an / 8.5 + 10^n*an
x = (1.5*10^n/8.5 - 1/8.5 + 10^n) * an
x = [(1.5/8.5 +1)*10^n - 1/8.5] * an
x ~ 11764... * an - we can eliminate an = 6, 7, 8, 9 because if the first digit is 6 then x = 70588... which doesn't have 6 as a first digit..... there will be a solution for each n = 16k - 1 and each leading digit an = 1, 2, 3, 4, 5.
-setting n=16 and an=1 in the above formula for x, we get
x = 1176470588235294. ,
1.5x = 1764705882352941 (1.5x does actually = 1764...............-multiplying this by 2, 3, 4 and 5 we get the other 16-digit solutions...
2352941176470588 * 1.5 = 3529411764705882
3529411764705882 * 1.5 = 5294117647058823
4705882352941176 * 1.5 = 7058823529411764
5882352941176470 * 1.5 = 8823529411764705
The other solutions are obtained by just putting on the same 16 numbers again and again to lengthen the number. The 32# solutions =
1176470588235294 1176470588235294 * 1.5 =
1764705882352941 1764705882352941
2352941176470588 2352941176470588 * 1.5 =
3529411764705882 3529411764705882
etc, etc.
2007-03-09 14:15:40 · answer #1 · answered by Dr. Nick 6 · 0⤊ 2⤋
The answer I come up with is 00.
If you multiply it 1.5 you will come up with 00, which is the first number with the first diget moved to the last place.
2007-03-09 15:30:20 · answer #2 · answered by Walking Man 6 · 0⤊ 0⤋
well, if you would tell me the difference between the two numbers, i can do it for you.
One thing's for sure, the last no. is 1.5 times the first answer and therefore must be larger than it.
But after, seeing Char's answer, i got some,
416 x 1.5 = 624
436 x 1.5 = 654
456 x 1.5 = 684
2007-03-09 17:09:28 · answer #3 · answered by Anonymous · 0⤊ 0⤋
456 x 1.5=684. You didn't mention anything about them having the same digits ,except for the 1st becoming the last.
2007-03-09 14:28:48 · answer #4 · answered by Charlie Kicksass 7 · 0⤊ 2⤋
err i hate math 5.1?
5 over 1?
1 times5??
2007-03-09 14:38:03 · answer #5 · answered by straightedge>sxe 2 · 0⤊ 0⤋
Who cares?
2007-03-09 14:27:17 · answer #6 · answered by Kathy 3 · 0⤊ 0⤋
can you give us some kinda clue other than we will be surprised by the answer??
2007-03-09 14:20:12 · answer #7 · answered by Happyness 2 · 0⤊ 0⤋
i'll just take the 2 points
2007-03-09 14:18:34 · answer #8 · answered by BOB H 4 · 0⤊ 0⤋
ok i know i am slow but dang! that went way over my head
2007-03-09 14:13:00 · answer #9 · answered by Anonymous · 0⤊ 0⤋
now i doubt my iq. if ever i find i will edit my answer and solve it for you, promise.
2007-03-09 15:29:06 · answer #10 · answered by prs 6 · 0⤊ 0⤋