# algebra

posted by .

How many reachable numbers are there between 1 and 1000?

• algebra -

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.

## Similar Questions

How many whole numbers are there between 99 and 1000?
2. ### Math

The product of 1000 whole numbers is 1000. What is the largest possible value the sum of these numbers can have?
3. ### Math

How many numbers between 1 and 1000 that has the #2 as its only factor
4. ### Math problems

i am two numbers, the sum of my numbers is 1000, the diffrence between my two numbers is 100
5. ### 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 …
6. ### 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. …
7. ### 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. …
8. ### 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. …
9. ### 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. …
10. ### 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. …

More Similar Questions