Re: numbers

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Posted by Brad Paul on October 23, 2002 at 18:45:24:

In Reply to: numbers posted by Jerry on October 23, 2002 at 13:58:42:

: Tim,Tom and Ted each have two numbered cards.
: Tim gives one of his cards to Tom, who gives one of his original cards to Ted.
: Ted in turn gives one of his original cards to Tim.
: Tim, who knew Ted's numbers, said "My total now could be 29 minimum or 48
: maximum."
: Tom, who knew Tim's numbers, said "My total now could be 27 minimum or 72
: maximum."
: Ted, who knew Tom's numbers, said "My total now could be 12 minimum or 62
: maximum".
: What numbers did each start with?

: Thank you for any help.
Your naming convention does not help. For variables I will use the
middle letter of each name. i.e. Tom=>o

I wrote the equations as I read you question:

Tim,Tom and Ted each have two numbered cards:
i₁, i₂ Tim's cards
o₁, o₂ Tom's cards
e₁, e₂ Ted's cards

Tim gives one of his cards to Tom, who gives one of his original cards to Ted.
Ted in turn gives one of his original cards to Tim:
Everyone will give away there #1 card. This is OK because we have not
specified it's value.

Tim, who knew Ted's numbers, said "My total now could be 29 minimum or 48
maximum."
i₂+e₁=29
i₂+e₂=48

Tom, who knew Tim's numbers, said "My total now could be 27 minimum or 72
maximum."
o₂+i₁=27
o₂+i₂=72

Ted, who knew Tom's numbers, said "My total now could be 12 minimum or 62
maximum".
e₂+o₁=12
e₂+o₂=62

Now you have 6 equations and 6 unknowns.

i₁ = -16
i₂ = 29
o₁ = -7
o₂ = 43
e₁ = 0
e₂ = 19

Follow Ups:

hmmm...check this, Mr P Denis Borris 20:17:31 10/23/02 (2)
- Re: hmmm...check this, Mr P Brad Paul 22:32:47 10/23/02 (1)
  - Thank you Mr B and Mr P..... Jerry 22:58:12 10/23/02 (0)

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: : Tim,Tom and Ted each have two numbered cards. : : Tim gives one of his cards to Tom, who gives one of his original cards to Ted. : : Ted in turn gives one of his original cards to Tim. : : Tim, who knew Ted's numbers, said "My total now could be 29 minimum or 48 : : maximum." : : Tom, who knew Tim's numbers, said "My total now could be 27 minimum or 72 : : maximum." : : Ted, who knew Tom's numbers, said "My total now could be 12 minimum or 62 : : maximum". : : What numbers did each start with? : : Thank you for any help. : Your naming convention does not help. For variables I will use the : middle letter of each name. i.e. Tom=>o : I wrote the equations as I read you question: : : Tim,Tom and Ted each have two numbered cards: : i1, i2 Tim's cards : o1, o2 Tom's cards : e1, e2 Ted's cards : Tim gives one of his cards to Tom, who gives one of his original cards to Ted. : Ted in turn gives one of his original cards to Tim: : Everyone will give away there #1 card. This is OK because we have not : specified it's value. : : Tim, who knew Ted's numbers, said "My total now could be 29 minimum or 48 : maximum." : i2+e1=29 : i2+e2=48 : Tom, who knew Tim's numbers, said "My total now could be 27 minimum or 72 : maximum." : o2+i1=27 : o2+i2=72 : : Ted, who knew Tom's numbers, said "My total now could be 12 minimum or 62 : maximum". : e2+o1=12 : e2+o2=62 : Now you have 6 equations and 6 unknowns. : i1 = -16 : i2 = 29 : o1 = -7 : o2 = 43 : e1 = 0 : e2 = 19

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