Freddie was in love with three girls. He couldn't decide who he wanted to give his heart to, so he sent all three a Valentine's card. But poor Freddie was out of luck, as each girl thought the card came from someone else and Freddie was left on the sideline.
From the clues below, can you work out the name of each potential sweetheart, the colour of each card Freddie sent and the name of the boy each girl believed the card was sent by?
Unluckily for Freddie, when Miss Jetson received her card, she thought it was from Adam. When Molly received her blue coloured card, she told Miss Hanson, and together they worked out who the card was from. It didn't occur to either of them that it was from Freddie! The girl who received the red card was convinced it came from Ethan. Neither Millie nor Miss Motson received a pink card.
First Names: Lily, Millie, Molly
Surnames : Hanson, Jetson, Motson
Colours : Blue, pink, red
Boys : Adam, Dylan, Ethan
Hint
Start by using (2) and (4) to find who received the pink card.
Answer
Lily Jetson Pink Adam
Millie Hanson Red Ethan
Molly Motson Blue Dylan
Reasoning
By (2), Molly received the Blue card:
Lily
Millie
Molly Blue
We now know that Molly didn't receive the Pink card, and by (4), neither did Millie, which means that Lily received the Pink card (and Millie received the Red):
Lily Pink
Millie Red
Molly Blue
By (4), the two girls who didn't receive the Pink card are Millie and Miss Motson, and we already know that Millie and Molly didn't receive the Pink Card, which means that Molly is Miss Motson.
Lily Pink
Millie Red
Molly Motson Blue
By (3), the Red card was thought to have come from Ethan:
Lily Pink
Millie Red Ethan
Molly Motson Blue
By (1), Miss Jetson's card was thought to have come from Adam, this can't be Molly (Motson), nor Millie (Ethan). So it must be Lily Jetson:
Lily Jetson Pink Adam
Millie Red Ethan
Molly Motson Blue
The puzzle can now be completed:
Lily Jetson Pink Adam
Millie Hanson Red Ethan
Molly Motson Blue Dylan
??
Puzzle 2
The BrainBashers printer isn't working correctly again (I must get it fixed!).
It's started printing O for odd numbers, and E for even numbers.
I know that all of the digits from 0 to 9 are used, and that the top row's digits add to 9.
Hint
The answer is 4 digits long, so what must G equal?
Answer
423 + 675 = 1098.
Reasoning
Remembering that:
even + even = even
odd + odd = even
even + odd = odd
To discuss individual letters, it's easiest to represent the sum as:
A B C
D E F +
————————
G H I J
A + D has to be over 9, which means that G = 1.
B + E = I, is even + odd = odd, which means that we can't have a carry from C + F (otherwise it would have been even + odd + 1, which is even).
The 1 has already gone, so the smallest possible value for either C or F is 3, which means that the other can't be 7 or 9 (otherwise we'd have a carry).
Therefore, C and F are 3 and 5, but we don't know which is which. But we do now know that J = 8.
A + D = H, is even + even = even, which means that we can't have a carry from B + E. Therefore, E can't be 9, as this would force a carry. So E = 7.
I is the only remaining odd number, so I = 9.
Which means that B = 2.
Neither A nor D can be 0 (otherwise we would have two of the same digit). So, H = 0.
Therefore, A and D are 4 and 6 (but we don't yet know which is which).
Since the top row's digits have to add to 9, A can't be 6, so A = 4, making C = 3.
This makes the sum 423 + 675 = 1098.
??
Puzzle 3
I started out on the journey from the forest with a full tank of fuel, 12 gallons exactly.
However, the moment I started out, the fuel tank sprung a leak. I travelled at 50 mph until I ran out of fuel exactly 4 hours later.
I know that the car does 25 miles for each gallon.
