Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

pythagoras123 Group Title

Peter and Jane take turns subtracting perfect squares from a given whole number and the person who subtracts the last number to get zero is the winner. If the whole number is 29, and Peter is the first player. what perfect number must he subtract in order for him to definitely win?

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    16 then Jane would have to subtract either 4 or 9, then jackpot for Peter

    • 2 years ago
  2. pythagoras123 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Er.. But Jane can subtract 1 and 16 also..

    • 2 years ago
  3. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Yeah ... it seems that way.

    • 2 years ago
  4. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    29 = 25 + 4 = 16 + 9 + 4 but there's no other way. If Jane subtracts 1 ... then it would ruin game.

    • 2 years ago
  5. pythagoras123 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    29= 16+1+9+1+1+1 Jane would then draw the last one

    • 2 years ago
  6. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    It might be best here to work in reverse. i.e. write down the outcome if, after your turn, Jane was left with 1, 2, 3, etc

    • 2 years ago
  7. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    you can then build up to a point where you can work out your best move

    • 2 years ago
  8. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    the other way seem to be 16+4+1+1+1+1+1+1+1+1+1 and 16+1+1+1+1+1+1+1+1+1+1+1+1+1 for Peter to win, I don't think peter will win if jane does not cooperate.

    • 2 years ago
  9. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    here is the table I worked out so far: after Peter moves, if he leaves: 1 => Jane wins 2 => Jane wins 3 => Peter wins 4 => Jane wins 5 => Jane wins 6 => Peter wins 7 => Jane wins 8 => Jane wins 9 => Jane wins 10 => Jane wins 11 => Peter wins 12 => Jane wins 13 => Peter wins so, as experimentX suggested, if Peter takes 16 first, that will leave 13 which means he would win.

    • 2 years ago
  10. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    it seems rather like game of odd - even

    • 2 years ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.