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
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Puzzle 3
My local shop wants to create a sign that says PUZZLES, and they have the following letters, each in a different colour:
P P P U U Z Z Z Z Z L L L L E S S
How many different ways can they make the sign?
Hint
There are 3 P's, so there are 3 different ways to start the word.
Answer
960.
Reasoning
Given: P P P U U Z Z Z Z Z L L L L E S S.
The order of the Z's is important. For example, we could chose a red one and a green one, so the order they appear in the sign has to be taken into consideration.
There are:
3 different P's that could be chosen.
2 different U's that could be chosen.
5 different Z's that could be chosen.
4 different Z's that could be chosen, as one has already been chosen.
4 different L's that could be chosen.
1 E that could be chosen.
2 different S's that could be chosen.
So there are 3 x 2 x 5 x 4 x 4 x 1 x 2 = 960 different ways to make the sign.
??
Puzzle 4
A kind old person decided to give 12 sweets to each of the adults in the town, and 8 sweets to each of the children.
Of the 612 people in the town, exactly half of the adults, and exactly three quarters of the children took the sweets.
How many sweets did the kind old person have to buy?
