Alex is a keen dog admirer and over the years has had a number of dogs.
Alex has had an Alsatian, a Dalmatian, a Poodle, and a Great Dane, but not necessarily in that order.
Alex had Jamie first.The Dalmatian was an adored pet before the Great Dane.Sammy, the Alsatian, was the second dog Alex loved.Whitney was owned before the Poodle.Jimmy was not a Great Dane.
Can you match the dogs to their names and find the order in which Alex had them?
Hint
Start by imaging a sign saying 'BrainBashers Puzzles And Illusions'.
Answer
I commissioned an artist to paint a sign for BrainBashers that said 'BrainBashers Puzzles And Illusions', however, they made a terrible mistake.
The gaps between 'Puzzles' and 'And', and 'And' and 'Illusions' weren't the same, so the sign seemed oddly out of balance.
??
Puzzle 19
During a recent BrainBashers thinking contest(!), the total number of points scored by the first six players was 103 and every score was above zero.
The first player scored half the points of the second player, who in turn scored 6 points fewer than the third player.
The third player in turn scored two thirds the points of the fourth player.
The fifth player managed to score the same number of points as the difference between the first and fourth player's points (larger − smaller).
Finally, the sixth player scored 14 fewer points than the fifth player.
Can you determine how many points the sixth player managed to score?
Hint
The fourth player is the key to this tricky question.
Answer
9 points.
Respectively the scores were 7, 14, 20, 30, 23, 9.
Reasoning
If we label the six players A, B, C, D, E, and F, we know that:
[1] A + B + C + D + E + F = 103
and from the clues:
A = B ÷ 2 B = C − 6 C = D x 2 ÷ 3 E = D − A F = E − 14
Note that it could be E = A − D or E = D − A, but using A − D we'd end up with a negative value for E later, which isn't allowed (so we'd have to try again with D − A anyway).
As we have no information for D, it's best to find all of the other letters in terms of D. These steps are left as an exercise (e.g. use C in the equation for B), but the result is:
A = ( D − 9) ÷ 3 B = (2D − 18) ÷ 3 C = (2D ) ÷ 3 D = (3D ) ÷ 3 E = (2D + 9) ÷ 3 F = (2D − 33) ÷ 3
Writing it as D = 3D ÷ 3 makes things slightly clearer in the next step.
