At the recent BrainBashers Mixed National Hurdle trials, ten contestants competed for the coveted BB Shield.
There were numerous judges who made sure that the results were accurate, from their notes can you determine who finished where?
Crystal Ball finished before May Eye and Mike Stup, while Leigh Vamessage was victorious over May Eye and Laura DeLand. Jack Pott was beaten by Holly Day, Mike Stup, and Justin Time. Laura DeLand was beaten by Mike Stup, May Eye, and Crystal Ball, whereas Joe King beat Holly Day and Jack Pott, but lost to Laura DeLand and Inga Hootz. Leigh Vamessage was beaten by Crystal Ball and Inga Hootz. Inga Hootz was beaten by Justin Time, who, in turn, lost to Crystal Ball, but beat Holly Day and Jack Pott. May Eye finished ahead of Mike Stup and Holly Day (who lost to Leigh Vamessage and Inga Hootz).
Hint
Rewrite the clues so that those who finished ahead are written first.
Answer
Crystal Ball (CB)
Justin Time (JT)
Inga Hootz (IH)
Leigh Vamessage (LV)
May Eye (ME)
Mike Stup (MS)
Laura DeLand (LD)
Joe King (JK)
Holly Day (HD)
Jack Pott (JP)
Reasoning
If we number the clues, write each name using two letters, and rewrite the clues so that those who finished ahead are written first:
CB beat ME and MSLV beat ME and LDHD, MS, and JT, all beat JPMS, ME, and CB, all beat LDJK beat HD and JPLD and IH both beat JKCB and IH both beat LVJT beat IHCB beat JTJT beat HD and JPME beat MS and HDLV and IH both beat HD
By (9): CB JT
By (8): CB JT IH
By (7): CB JT IH LV
By (2): CB JT IH LV ME
By (11): CB JT IH LV ME MS
By (4): CB JT IH LV ME MS LD
By (6): CB JT IH LV ME MS LD JK
By (5): CB JT IH LV ME MS LD JK HD
By (3): CB JT IH LV ME MS LD JK HD JP
??
Puzzle 200
Farmer Stone is quite an eccentric dairy farmer.
He originally had a total of 54 gallons of milk in three churns, and he wanted to make sure each churn contained 18 gallons of milk.
In order to do this, he did the following:
First, he poured 1/4 of the first churn into the second churn. He then poured 1/2 of the second churn into the third churn. Finally, he poured 1/3 of the third churn into the first churn.
How many gallons did each churn contain before Farmer Stone started pouring?
Hint
Try working backwards, with each churn containing 18 gallons.
Answer
12, 33, and 9 gallons respectively for churns 1, 2, and 3.
Reasoning
Working backwards, at the end after Pour 3, the churns (C1, C2, C3) contained:
C1 C2 C3
————————————
18 18 18 after Pour 3
Pour3 was 1/3 of C3 into C1, the remaining 2/3 has to be the 18 gallons left in C3 after the pour, which means that 1/3 is 9 gallons. So 9 gallons was poured from C3 into C1. Before Pour3, C1 must have contained 9 gallons, and C3 contained 27 gallons.
C1 C2 C3
————————————
9 18 27 after Pour 2
18 18 18 after Pour 3
Pour2 was 1/2 of C2 into C3, the remaining 1/2 has to be the 18 gallons left in C2 after the pour, which means that 1/2 is 18 gallons. So 18 gallons was poured from C2 into C3. Before Pour2, C2 must have contained 36 gallons, and C3 contained 9 gallons.
C1 C2 C3
————————————
9 36 9 after Pour 1
9 18 27 after Pour 2
18 18 18 after Pour 3
Pour1 was 1/4 of C1 into C2, the remaining 3/4 has to be the 9 gallons left in C1 after the pour, which means that 1/4 is 3 gallons. So 3 gallons was poured from C1 into C2. Before Pour2, C1 must have contained 12 gallons, and C2 contained 33 gallons.
C1 C2 C3
————————————
12 33 9 at the start
9 36 9 after Pour 1
9 18 27 after Pour 2
18 18 18 after Pour 3
