Hint
This is quite a tricky puzzle, and knowledge of algebra would certainly help.
Answer
The children tickets were £14, and the adult tickets were £18.
Reasoning
There are a number of methods for solving this problem, including:
Using a spreadsheet.Using a computer program.Using the intersection of lines on a graph.Using an online equation solver.Solving simultaneous equations using algebra.Solving simultaneous equations using inverse matrices.
Here is my solution using simultaneous equations and algebra.
First construct two algebraic equations, where 'c' is the number of children, and 'a' is the number of adults:
4296c + 2143 x 18 = 98718 4296c + 38574 = 98718 4296c = 60144 c = 14
Double-Checking
c = 14 and a = 18
4,296 x 14 + 2,143 x 18 = 98,718
and
5,146 x 14 + 2,807 x 18 = 122,570
?
Puzzle 18
Below are safari animals, however, each letter has been replaced by its position in the alphabet, but the spaces between the resulting numbers have been removed.
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 20
Matthew Shelborn frequently has to travel for his company, which gives him a chance to meet many people from all parts of the USA. In April, Matthew flew to five different US cities on business and he flew a different airline each time. During each trip he chatted with the person next to him, and no two people he talked to were in the same profession.
From the information, can you determine the date Matthew made each flight (each was on a Monday exactly one week apart starting on April 2nd), the airline he flew, his destination, and the profession of the person who sat next to him on each flight?
Three consecutive flights were, in order from first to last, the flight Matthew took with WTA Airways, the flight where he sat next to the teacher, and the flight he took to Atlanta. Matthew sat beside the sports coach on a flight some time earlier in the month than the one he took to Seattle. The week he flew Air Express was some time earlier in the month than the trip to Boston, which was some time earlier in the month than the trip where he sat next to the ballet dancer. It wasn't on the trip to San Diego where Matthew sat next to the doctor. Matthew didn't fly Skyways on his trip to Seattle, and he didn't fly WTA Airways on the trip where he sat next to the sports coach. Atlanta was not Matthew's destination on the trip where he made the acquaintance of the ballet dancer. The Fly America flight was exactly two weeks before the flight where Matthew passed the time chatting with the attorney.
Dates : April 2nd, April 9th, April 16th, April 23rd, April 30th
Airline : Air Express, Fly America, MidUSA Air, Skyways, WTA Airways
Destination : Atlanta, Boston, Chicago, San Diego, Seattle
Seat Mate : Attorney, Ballet Dancer, Doctor, Sports Coach, Teacher
Answer Date Airline Destination Seat Mate April 2nd WTA Airways Chicago Doctor April 9th Fly America San Diego Teacher April 16th Air Express Atlanta Sports Coach April 23rd Skyways Boston Attorney April 30th MidUSA Air Seattle Ballet Dancer
The trip to Atlanta (1), the trip where Matthew sat next to the ballet dancer (3), and the trip where Matthew sat next to the attorney (7) were among the last three trips [April 16th, 23rd, and 30th (intro)], and the trip to Atlanta wasn't the one where he met the ballet dancer (6) or the attorney. He flew WTA Airways exactly two weeks before the one to Atlanta, and he flew Fly America exactly two weeks before he sat by the attorney (7), so, these three are separate flights, in some order.
He didn't sit by the teacher on the trip to Atlanta (1), so the flight were he sat by the teacher was on one of the first two flights [April 2nd and April 9th (intro)], but it wasn't first [after WTA Airways](1), therefore, April 2nd flight was the WTA Airways flight, the one where he sat by the teacher was the April 9th flight, and the one to Atlanta was the April 16th flight, and he sat by the ballet dancer and attorney on the April 23rd and April 30th flight, in some order.
He didn't sit beside the sports coach on the WTA Airways flight (5) so that wasn't April 2nd, he sat beside the sports coach on the Atlanta flight [April 16th] and it was the April 2nd flight where he sat next to the doctor.
April 2nd [first flight, WTA Airways, doctor] wasn't to Seattle (2), Boston (3), or San Diego (4), that flight was to Chicago.
The April 9th flight wasn't to Seattle [after sports coach which was April 16th] or to Boston [after Air Express, which would have to be April 2nd, but WTA Airways was April 2nd (1)](3), so, on April 9th he flew to San Diego.
Boston wasn't the last destination (3), so it was his destination on April 23rd and Seattle was his destination on April 30th.
Boston [April 23rd] was before the one where he sat by the ballet dancer (3), so he sat by the ballet dancer on April 30th flight to Seattle, and it was on the April 23rd flight to Boston that he sat by the attorney.
Since he sat by the attorney on the April 23rd flight, then he flew Fly America on the 9th [exactly two weeks before](7).
He flew Air Express before the flight when he flew to Boston [April 23rd](3) so he flew Air Express on the 16th.
He didn't fly Skyways to Seattle [April 30th](5), so, he flew Skyways to Boston on the 23rd and his last flight that month was on MidUSA Air (intro).
