Possible values of X and Y for the problem

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Discussion Overview

The discussion revolves around finding possible values for whole numbers X and Y based on a set of conditions involving their sums, differences, products, and a specific type of number referred to as a "twin number." The participants explore various approaches to solving this problem, including trial and error and other methods.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant states that X and Y are whole numbers and proposes conditions: X + Y equals a square number, X - Y equals a prime number, X * Y equals a twin number, and X / Y equals an irrational number.
  • Another participant points out that if X and Y are whole numbers, then X / Y cannot be irrational, challenging the initial conditions.
  • Several participants discuss the implications of the first three conditions after removing the fourth, questioning how to approach the problem systematically.
  • One participant suggests starting with the product condition (X * Y) to derive possible values for X and Y, indicating that one of them could be 1 or another number.
  • Another participant notes that while considering Y as 11, they find that not all values of X satisfy the other conditions, leading to frustration with the ad hoc nature of their attempts.
  • There is mention of the possibility of multiple values for X and Y, with one participant asserting that 1 and 11 are not the only solutions.
  • A later reply clarifies a misunderstanding regarding the term "twin number," suggesting that it refers to two digits being the same rather than a semiprime.

Areas of Agreement / Disagreement

Participants express differing views on the validity of the initial conditions and the methods for solving the problem. There is no consensus on a definitive solution, and multiple approaches are discussed without agreement on their effectiveness.

Contextual Notes

Participants acknowledge the arbitrary nature of the conditions set forth and the challenges in deriving a systematic solution. The discussion reflects uncertainty regarding the existence of solutions under the given constraints.

issac newton
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X and Y are whole nos
X+Y= square of a no.
X-Y=prime no.
X*Y=twin no. (eg 77)
X/Y=irrational no.

how to solve such kind of problems apart from trial n error basis(ad hoc) ?
 
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If x and y are whole numbers, then x/y can't be irrational.
 
sorry abt the fourth condition. what if first 3 conditions are considered ??

X+Y= square of a no.
X-Y=prime no.
X*Y=twin no. (eg 77)

what are the possible values of x and y. how to approach such a problem to narrow down our answers ??
 
Issac Newton said:
sorry abt the fourth condition. what if first 3 conditions are considered ??

X+Y= square of a no.
X-Y=prime no.
X*Y=twin no. (eg 77)

what are the possible values of x and y. how to approach such a problem to narrow down our answers ??
Start with the last condition. What does that allow you to say about X and Y? (either one of them is 1 or ...?)
 
The value of x or y can be 1 or 11. but all values of x with y being 1,will not satisfy the other two conditions. like
99*1=99 but

99-1=98 not a prime.

so i considered y=11, thus x+y should b greater than 11 n a square no: so it starts from 16(x+y) and goes on... but this method is ad hoc n i did not get any solution for this because 1 condition always fails for some x value.

is there any equation solving method and also can this question have a solution if at all ??
 
Issac Newton said:
The value of x or y can be 1 or 11. but all values of x with y being 1, will not satisfy the other two conditions. like
99*1=99 but

99-1=98 not a prime.

so i considered y=11, thus x+y should b greater than 11 n a square no: so it starts from 16(x+y) and goes on... but this method is ad hoc n i did not get any solution for this because 1 condition always fails for some x value.

is there any equation solving method and also can this question have a solution if at all ??

99 = 3 * 33, so 1 and 11 aren't the only values x or y can take.

There's 1 solution to your problem.

Don't be surprised that you're getting "ad hoc" methods, you've thrown together a few random arbitrary conditions, especially the "twin number" bit.
 
thank u abacus.

i think the answer is 22 and 3.

22*3=66

22-3=19

22+3=25
 
Ok, I misunderstood. I thought by "twin" number you meant a semiprime. You just mean two digits the same, right?
Typically there are no equations for these sorts of problems. The technique is to start with the pieces of information that narrow down the possibilities fastest.
Btw, for X*Y there are also possibilities like 3*22, etc.
 

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