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 At the party (Posted on 2011-07-22)
At the party staged by 3 young couples the following leaflet was distributed among the guests:

"Who now are 3, will soon be 6
But how we've chosen you may know
As soon as you have guessed it.

Tom, who is older than Jim, is Dorothy's brother ,
Virginia is the oldest girl,
The total age of each couple-to-be is the same,
No two of us are of the same age,
Jim and Lisa together are as old as Bill and Dorothy together."

Who got engaged to whom?

Abridged from: 101 PUZZLES BY C.R.WYLIE Jr (1957)

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 solution Comment 2 of 2 |

If the match between the totals J+L and B+D were the result of Jim pairing with Lisa and Bill with Dorothy, then Tom would be paired with Virginia. But that's not possible, as the oldest girl must be matched with the youngest guy.

So let's lay out a possible order. This is the simplest:

`10  -  1 9  -  2 8  -  3`

where the numbers represent years above some baseline.

Each row represents a pairing of an engaged couple. Arbitrarily the higher numbers are for the guys.

9+1 = 8+2 so those diagonals match, and can represent J+L and B+D. As these represent, on the male side, Jim and Bill, Tom must be the 10 at the top. Dorothy cannot then be the 1, so that must be Lisa. In sum:

`      Tom 10  -  1 Lisa      Jim  9  -  2 Dorothy     Bill  8  -  3 Virginia`

Of course the sizes of the relative ages is just an example of the possibilities, but the pairing is as shown on these three lines.

 Posted by Charlie on 2011-07-22 14:08:42

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