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Puzzle 129
Yesterday I was asked to buy some stamps.
In the land of BrainBashers, stamps are available in denominations of 4p, 5p, 7p, 12p, and 19p (just the five different values).
For three denominations of stamps, I was asked to buy six of each. For the other two denominations. I was asked to buy ten of each.
Unfortunately, I forgot which I was supposed to buy six of, and which to buy ten of!
Luckily I had been given the exact money required to buy the stamps, £3.50, so the shopkeeper was able to work out the stamps I needed.
During a recent music festival, four DJs entered the mixing contest.
Each wore a number, either 1, 2, 3 or 4 and their decks were different colours.
DJ Skinf Lint came first, and only one DJ wore the same number as the position he finished in. DJ Slam Dunk wore number 1. The DJ who wore number 2 had a red deck and DJ Jam Jar didn't have a yellow deck. The DJ who came last had a blue deck. DJ Park'n Ride beat DJ Slam Dunk. The DJ who wore number 1 had a green deck and the DJ who came second wore number 3.
Can you determine who came where, which number they wore and the colour of their deck?
At last month's rehearsal, four top athletes competed in two 400-metre qualifiers.
As the results were expected to be mislaid, various notes were taken to ensure the accuracy of the overall placings:
No one finished both races in the same position. In both races, Sam beat the runner whose surname was Watson. Billie Taylor came third in the second race, and Pat came last in the first race. In the second race, the athlete whose surname was Arnold won, and the athlete whose surname was Bowler came last. In the first race, Billie beat Jamie, but Jamie beat Sam.
Can you determine who finished where in each of the races?
Answer
Race1 Race2
————————————————————————
#1 Billie Sam
Taylor Arnold
————————————————————————
#2 Jamie Pat
Bowler Watson
————————————————————————
#3 Sam Billie
Arnold Taylor
————————————————————————
#4 Pat Jamie
Watson Bowler
Reasoning
The four names were: Billie, Jamie, Pat, Sam
The four contestants were: Arnold, Bowler, Taylor, Watson.
By (3), Billie Taylor came third in the second race, and Pat came last in the first race, giving:
Race1 Race2
————————————————————————
#1
————————————————————————
#2
————————————————————————
#3 Billie
Taylor
————————————————————————
#4 Pat
By (5), in the first race Billie beat Jamie, and Jamie beat Sam, giving:
Race1 Race2
————————————————————————
#1 Billie
Taylor
————————————————————————
#2 Jamie
————————————————————————
#3 Sam Billie
Taylor
————————————————————————
#4 Pat
By (2), Sam beat the runner with the surname Watson in the first race, which means that Pat's surname is Watson, giving:
Race1 Race2
————————————————————————
#1 Billie
Taylor
————————————————————————
#2 Jamie
————————————————————————
#3 Sam Billie
Taylor
————————————————————————
#4 Pat
Watson
By (1), Pat can't have also finished in last place in race 2, and by (2), Sam beat the Pat Watson, so Pat must have finished in second place in race 2. And Sam came first, therefore Jamie came last, giving:
Race1 Race2
————————————————————————
#1 Billie Sam
Taylor
————————————————————————
#2 Jamie Pat
Watson
————————————————————————
#3 Sam Billie
Taylor
————————————————————————
#4 Pat Jamie
Watson
By (4), in the second race the athlete whose surname was Arnold won, and the athlete whose surname was Bowler came last, so we know Sam and Jamie's surnames, and we can complete the grid:
Race1 Race2
————————————————————————
#1 Billie Sam
Taylor Arnold
————————————————————————
#2 Jamie Pat
Bowler Watson
————————————————————————
#3 Sam Billie
Arnold Taylor
————————————————————————
#4 Pat Jamie
Watson Bowler
??
Puzzle 132
What is the minimum number of queens required on a chessboard such that all squares are attacked?
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It is now three years since I first asked for support, and I would like to sincerely thank everyone who has helped me. BrainBashers doesn't show adverts, and I continue to depend on the ongoing support from everyone who enjoys the site.
