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.
Four friends were competing in the internationally renowned BrainBashers Bog Snorkelling competition.
As usual, the judges were a little careless and, once again, they managed to lose the results.
Luckily, a number of spectators were able to remember the following snippets of information:
Only one person wore the same number as the position they finished. Gary, who didn't wear green, beat Barry. Larry beat the person who wore yellow. The person who wore number 3, wore green. The person who wore number 2 finished first, whereas Harry came last. The person who finished second wore green, Barry wore yellow, and the person wearing red beat the person wearing blue.
Can you work out who finished where, and the number and colour they wore?
Hint
Start by looking at clue (5), and then at the first part of clue (6).
Answer # Name Wore Colour
1 Gary 2 red
2 Larry 3 green
3 Barry 1 yellow
4 Harry 4 blue
Reasoning
By (5), the winner wore #2, and Harry finished last: # Name Wore Colour
1 2
2
3
4 Harry
By (6), the person who finished second wore green, and by (4), wore #3: # Name Wore Colour
1 2
2 3 green
3
4 Harry
By (1), only the person in last place could have worn the same number as the position they finished: # Name Wore Colour
1 2
2 3 green
3 1
4 Harry 4
By (3), Gary didn't wear green (so can't have finished second) and beat Barry (so can't have finished third), which means that he must have finished first. # Name Wore Colour
1 Gary 2
2 3 green
3 1
4 Harry 4
By (6), Barry wore yellow, so must have finished third: # Name Wore Colour
1 Gary 2
2 3 green
3 Barry 1 yellow
4 Harry 4
By (6) the person wearing red beat the person wearing blue, giving: # Name Wore Colour
1 Gary 2 red
2 Larry 3 green
3 Barry 1 yellow
4 Harry 4 blue
