At the recent interdepartmental jam making contest, four lucky candidates took part to make the juiciest strawberry jam.
As it happens, the person who came last was the oldest. Glen was three years older than the person who came second. Drew was neither the oldest nor the youngest. Emery finished ahead of the 27-year-old, but didn't win. Alex was also unlucky this time, and didn't win either.
The ages of the contestants were 24, 27, 30 and 32.
Can you work out who finished where, and how old they were?
Answer # Name Age
1 Drew 30
2 Emery 24
3 Glen 27
4 Alex 32
Reasoning
By (2), because Glen was three years older, the person in 2nd place was either 24 or 27.
But 2nd place can't have been 27, because, by (4), Emery was ahead, but didn't win.
So 2nd place was 24, and Glen was 27.
By (3), Drew could only be 27 or 30, but we now know what Glen was 27, so Drew was 30.
By (1), the person who came last was 32:
1
2 24
3
4 32
By (4), the 27-year-old can't have won,
1 Drew 30
2 24
3 Glen 27
4 32
By (4), Emery beat the 27-year-old:
1 Drew 30
2 Emery 24
3 Glen 27
4 32
Leaving Alex in last place.
1 Drew 30
2 Emery 24
3 Glen 27
4 Alex 32
?
Puzzle 198
Place letters into the grid such that every row, column, and 2 x 2 block has letters (in any order) that form a common word. Each letter is only used once, and no letter is repeated in the rows / cols / blocks.
Letters allowed: S O N A T A
R
E
B
S
W
K
R
E
P
Z
Note: this puzzle is not interactive, and the squares cannot be clicked.
Reasoning
If we convert the question to algebra, we have:
((n^2 + 4) x 2 − 3) x 4 − n = 20
Expanding the brackets and simplifying gives:
(2n^2 + 8 − 3) x 4 − n = 20
(2n^2 + 5) x 4 − n = 20
8n^2 + 20 − n = 20
8n^2 − n = 0 (*)
8n − 1 = 0
8n = 1
n = 1/8
In the equation marked (*) zero is also a potential solution, but as the question tells us that we "Start with a number larger than 0" we know that n can't be 0, and therefore we can safely divide by n.
