Don't we have a favourite colour and a favourite number?

One of the first observations to make is that even though Vicky is a girl which means her favourite number is either 1, 3 or 5 from fact 1, fact 6 will however knock out the possibility that her favourite number is 3. This is because 3 is in the middle of 1 to 5 so 3 differs from all the other numbers by at most 2. This means her favourite number is either 1 or 5.

From fact 5, we have two scenarios, either:

• the person who likes orange likes the number 4 while Zachary likes the number 2 or
• the person who likes orange likes the number 2 while Zachary likes the number 1.

If it were the latter, then Vicky's favourite number must be 5. But employing fact 6, the person who likes blue would like the number 2, which contradicts with our assumption that the person who likes the number 2 likes orange. Thus we can safely assume the former. The person who likes orange likes the number 4 while Zachary likes the number 2. Now employing fact 6, considering that Vicky's favourite number is 1 or 5, if her favourite number is 1, then the person who likes blue likes the number 4, which contradicts with the fact that the person who likes the number 4 likes orange. Thus Vicky's favourite number must be 5 and the one who likes blue likes the number 2 (Zachary).

From fact 2, the person who likes green likes either 1 or 4 but 4 is already taken by the person who likes orange. Thus the person who likes green likes the number 1. Next, the person who likes orange cannot be Vicky or Zachary considering that they like the number 5 and 2 respectively but the person who likes orange likes the number 4. It also cannot be Yasmine considering that Yasmine, being a girl, likes an odd number (fact 1) but 4 is an even number. Employing fact 3, if William likes orange, then the person who likes red likes the number 2 which contradicts with the fact that the person who likes the number 2 likes blue. Thus the only possible person who likes 4 and orange is Xavier.

Finally, if William's favourite number is 3, then employing fact 3, the one who likes red must like the number 5 (Vicky) considering that the person who likes 1 already likes green. But then the only possible colour left for William would be purple (green-1, blue-2, orange-4, red-5) which contradicts with fact 4. Thus William's favourite number must be 1 which means the one who likes red must like the number 3. Now the only possible colour left for Vicky is purple, which means $\boxed{Yasmine}$ likes the colour red.

Clue 5 : The person who likes orange likes a number that is double Zachary's favourite number.
Orange = { 2, 4 } while Z = { 1, 2 }

Clue 1 : Each girl likes an odd number.

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Clue 6 : The person who likes blue likes a number that differs from Vicky's favourite number by three.
V = { 1, 5 } & Blue = { 2, 4 } & Y = { 1, 3, 5 }

Therefore, Blue and Orange are boys' colours, though Z didn't like Orange.

Clue 2 : The person who likes green likes a perfect square.
Green = { 1, 4 } , but we already have { Blue, Orange } = { 2, 4 } , so 4 can either be Blue or Orange but not Green, thus Green = { 1 }.

Clue 3 : The person who likes red likes a number that differs from William's favourite number by two.
Since both even numbers already have colours assigned to each, of which Red is neither, then both Red and W must have both been paired to odd numbers. Therefore, Red must be girl's colour.

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Clue 4 : The person who likes purple is a girl.
{ V , Y } = { Red, Purple } = { 3, 5 }

W = Green = 1
Z = Blue = 2
X = Orange = 4
V = 5 ≠ Red = Purple
Y = Red = 3