Tag Archives: Algebra

[Soln] Problem involving two coins

Posted on 18 Jan 2023 by kjytay

Let such that . Assume we have two coins such that the probability of coin 1 landing on heads (after flipping it) is and the probability of coin 2 landing on heads is . For what values of do there … Continue reading →

Posted in Random | Tagged , | Leave a comment

Problem involving two coins

Posted on 17 Jan 2023 by kjytay

Let such that . Assume we have two coins such that the probability of coin 1 landing on heads (after flipping it) is and the probability of coin 2 landing on heads is . For what values of do there … Continue reading →

Posted in Random | Tagged , | Leave a comment

[Soln] 2016 Putnam Problem B1

Posted on 19 Dec 2016 by kjytay

2016 Putnam B1. Let be the sequence such that and for , (as usual, the function is the natural logarithm. Show that the infinite series converges and find its sum.

Posted in Undergraduate, USA | Tagged , , , | Leave a comment

2016 Putnam Problem B1

Posted on 18 Dec 2016 by kjytay

2016 Putnam B1. Let be the sequence such that and for , (as usual, the function is the natural logarithm. Show that the infinite series converges and find its sum.

Posted in Undergraduate, USA | Tagged , , , | Leave a comment

[Soln] 2013 AIME I Problem 10

Posted on 13 Jun 2016 by kjytay

2013 AIME I 10. There are nonzero integers , , , and  such that the complex number  is a zero of the polynomial . For each possible combination of  and , let  be the sum of the zeroes of .Find the sum … Continue reading →

Posted in Grade 12, USA | Tagged , , , | Leave a comment

2013 AIME I Problem 10

Posted on 13 Jun 2016 by kjytay

2013 AIME I 10. There are nonzero integers , , , and  such that the complex number  is a zero of the polynomial . For each possible combination of  and , let  be the sum of the zeroes of .Find the sum … Continue reading →

Posted in Grade 12, USA | Tagged , , , | Leave a comment

[Soln] 2013 AIME I Problem 8

Posted on 11 Jun 2016 by kjytay

2013 AIME I 8. The domain of the function  is a closed interval of length , where  and  are positive integers and . Find the remainder when the smallest possible sum  is divided by 1000.

Posted in Grade 12, USA | Tagged , , , | Leave a comment

2013 AIME I Problem 8

Posted on 11 Jun 2016 by kjytay

2013 AIME I 8. The domain of the function  is a closed interval of length , where  and  are positive integers and . Find the remainder when the smallest possible sum  is divided by 1000.

Posted in Grade 12, USA | Tagged , , , | Leave a comment

[Soln] 2013 AIME I Problem 5

Posted on 8 Jun 2016 by kjytay

2013 AIME I 5. The real root of the equation can be written in the form , where , , and  are positive integers. Find .

Posted in Grade 12, USA | Tagged , , | Leave a comment

2013 AIME I Problem 5

Posted on 8 Jun 2016 by kjytay

2013 AIME I 5. The real root of the equation can be written in the form , where , , and  are positive integers. Find .

Posted in Grade 12, USA | Tagged , , | Leave a comment