# Grantstein's Challenge

by mathgrant

By 8, the Brit has a red house and 5 children.

By 4 and 13, she is west of Hope, who has the One Way sign.

By 10, the American is west of her.

By 6, the French woman is also west of her.

Now, consider Rosanna. She is not French (by 3) or Australian (by 7).

She is also not the Canadian, because there is nowhere to put her. By the information we have so far about the Brit, a Canadian Rosanna would have to be either on one end (in which case she doesn't have two neighbors) or next to the Brit (who is not French or the woman with 2 children).

Assume Rosanna is the American. Now there must be a third house west of the Brit (with 2 children). In order for the Canadian to have two neighbors, she can't be on either end, so she must be in the middle house, and the French woman must be on the west end. But that leaves Hope as the Australian, which contradicts 7.

So, Rosanna is the Brit. From 3, the French woman is her neighbor. Also Hope is not the American or French woman (because she's east of Rosanna), or the Australian (by 7), so she must be the Canadian. Since the Canadian has two neighbors, she can't be on the end (and therefore must be next to Rosanna and have 2 children), and so Ellen from Australia must be on the east end. Since Sarah is next to the woman with 5 children, and obviously isn't Hope, that makes her the French woman, and gives the American (Lucy with the yellow house, by elimination) the Speed Limit sign.

By 1, Hope the Canadian is next to the White house and the Hospital sign, but obviously Rosanna does not have the White house, so she has the Hospital sign and Ellen has the White house. Now Lucy, Rosanna, and Hope have signs, and the Stop sign is not Sarah's (by 5), so Ellen must have it, and Sarah has the Railroad Crossing sign.

By 12, there is a woman between the Blue house and the house with four children. This must be Rosanna by elimination. Since Hope already has the 2 children, she must have the Blue house, and Sarah has 4 children and is in the Green house. Finally, by 2, Lucy must have 3 children and Ellen 1.

So, the solution from west to east is:

Lucy - US, Yellow, 3, Speed Limit

Sarah - France, Green, 4, Railroad Crossing

Rosanna - UK, Red, 5, Hospital

Hope - Canada, Blue, 2, One Way

Ellen - Australia, White, 1, Stop