algebra
posted by Anonymous...please help! .
How many reachable numbers are there between 1 and 1000?

following the pattern, the assumptions could be:
1>3
3>4 or 5
4>12 or 5>15
12>13 or 14 and 15>16 or 17
.
.
. and so on..
now assuming that respective stages comprises of numbers(let it be x) to which 1 and 2 was added, followed by the numbers formed after multiplying 3 to x
so,
at stage 1, numbers are:
1(x),3(3x)
at stage 2:
4,5(3x+1,3x+2);12,15[3(3x+1),3(3x+2)]
at stage 3:
13,14,16,17,39,42,48,41
and so on and so forth.
notice that at stage 1, total numbers were 2. At stage 2, total nubers were 2^2. At stage 3 total numbers were 2^3.
it is thus a simple case of geometric progression.
now we have to limit this progression till 1000.
thus, if we consider the chain of the lowest numbers, it will correspond to:
(((((3+1)*3)+1)*3)+1)*3)+1)*3)
this equals 363 and stops at stage 5.
363*3=1089, which exceeds 1000, thus all the chains cannot exceed after stage 5. That means number of assumptions= 2+ 2^2 + 2^3 + 2^4 + 2^5...which equals 62. now at stage 5, each number can be added with either 1 or 2, but cannot be multiplied further by 3.
Thus at stage 5, we will have 16 numbers to which 1 or 2 can be added. thus we have 16*2=32 more numbers.
This finally gives us a total of 32+62=94 numbers.
i know i'm not that clear but i'm sure if u practically solve the way i did it u'll get it :D
and yes...thnx for giving such a mind boggling question.
Respond to this Question
Similar Questions

6 grade math
How many whole numbers are there between 99 and 1000? 
Math
The product of 1000 whole numbers is 1000. What is the largest possible value the sum of these numbers can have? 
Math
How many numbers between 1 and 1000 that has the #2 as its only factor 
Math problems
i am two numbers, the sum of my numbers is 1000, the diffrence between my two numbers is 100 
math
What is the minimum value of N that will make this statement true: If we pick any N composite numbers from 1 to 1000, then we can find 2 numbers whose greatest common divisor is not 1. Details and assumptions You may use the fact that … 
Algebra
Alan and Bob are playing with numbers. Starting with the number n=1 they take turns performing arithmetic manipulations with n. Alan goes first and always multiplies n by 3. Bob adds 1 or 2 to the number n, depending on a coin toss. … 
Algebra
Alan and Bob are playing with numbers. Starting with the number n=1 they take turns performing arithmetic manipulations with n. Alan goes first and always multiplies n by 3. Bob adds 1 or 2 to the number n, depending on a coin toss. … 
arithmetic
Alan and Bob are playing with numbers. Starting with the number n=1 they take turns performing arithmetic manipulations with n. Alan goes first and always multiplies n by 3. Bob adds 1 or 2 to the number n, depending on a coin toss. … 
Algebra
Alan and Bob are playing with numbers. Starting with the number n=1 they take turns performing arithmetic manipulations with n. Alan goes first and always multiplies n by 3. Bob adds 1 or 2 to the number n, depending on a coin toss. … 
math
Alan and Bob are playing with numbers. Starting with the number n=1 they take turns performing arithmetic manipulations with n. Alan goes first and always multiplies n by 3. Bob adds 1 or 2 to the number n, depending on a coin toss. …