Puzzles for Settle District U3A Mathematical Puzzles

Sessions take place on Tuesdays at 2pm in the Victoria Hall. Dates for spring 2010 (i.e. 2nd and last Tuesday of each month):

Tu 12 Jan        Tu 26 Jan        Tu 9 Feb        Tu 23 Feb

Tu 9 Mar        Tu 30 Mar        Tu 13 Apr        Tu 27 Apr

Tu 11 May        Tu 25 May        Tu 8 Jun        Tu 29 Jun

The group looks at puzzles from a wide variety of sources. Anyone is free to bring a puzzle for others to talk about and possibly solve. Sessions are surprisingly jolly.

Here is some food for thought that is likely to feature in the next few sessions.

• Electoral systems — some ideas on the subject ^NEW
• Snooker and pool margins for error
• Owt for Nowt — a queston of finance from Chris Petrie
• 4 × 4 — a queston of colours from Chris Petrie
• Random Matrix from New Scientist — are we convinced, sceptical, baffled? You might even like to look at the Riemann hypothesis.
• Here is a problem and solution from Chris Maslanka in the Guardian, along with some more food for thought.
• ENIGMA 1585 Diving points — from New Scientist
• ENIGMA 1584 Trisquare — from New Scientist
• Cars and most other road vehicles have differentials to allow them to go round corners, but trains have solid axles to allow them to go round corners — except pseudo-buses at Carnforth! I wonder what are the conditions under which the flanges touch the rails?
  Here is a link to useful info.
• ENIGMA 1583 Have a good day — from New Scientist answer from Chris
• ENIGMA 1582 Bit tricky — from New Scientist answer from Chris
• ENIGMA 1580 If you knew what I knew... — from New Scientist answer from Chris
• ENIGMA 1578 About turn — from New Scientist
• Dirac was good at binary arithmetic
• Dividing by 7 is not as easy to test for as other single digit divisors.
• Pizza portions An article from New Scientist. Can we prove it? Here is a cutting analysis from Chris, and
  here is Chris’s sequel for division between 2 diners (with picture), and
  here is Chris’s sequel for division between 3 diners (with picture).
• ENIGMA 1574 Doubly square dates — from New Scientist Here is a rounded analysis from Chris, and the official New Scientist solution
• Bayesian statistics are described in this New Scientist article. There is more material on statistics in bit.ly/1c3tgj and this New Scientist article.
• ENIGMA 1570 Set of Cubes — from New Scientist — answer to part 2 from Chris
• A window problem from John Hughes.
• ENIGMA 1569 Cardiology — from New Scientist — thoughts from David
• ENIGMA 1566 Consistently older — from New Scientist
• ENIGMA 1565 It’s a rollover — from New Scientist — the answer from Chris and David
• Is the moon escaping?
• ENIGMA 1561 Some check! — from New Scientist — the answer which emerged during our September 2009 session
• ENIGMA 1563 Drawing a line — from New Scientist

• ENIGMA 1541 Box clever — from New Scientist
• ENIGMA 1540 On the run — from New Scientist
• ENIGMA 1537 A name game — from New Scientist — analysis from Chris

• Another straight line drawing machine discovered by Robin Corbett.

Here is a list of fairly recent subjects, most of which we have solved.

• ENIGMA 1538 Six factors — from New Scientist — analysis from David
• Two towers a variant on the towers of Hanoi
• ENIGMA 1534 The hare and the tortoise from New Scientist — solution from Chris
• ENIGMA 1535 Back to front from New Scientist — solution from Chris and David
• Lead Balloons revisted — Here is an article from New Scientist
• ENIGMA 1532 Just reflecting from New Scientist — solution from DH — and a draughtman’s approach from Keith.
• Gravitational SlingShots — an article found by John Hughes
• Leonardo da Vinci’s bridge. If you apply a vertical load to the top centre bar, what is downward force exerted on the horizontal bars? — Analysis.
• ENIGMA 1511 Way out from New Scientist
• ENIGMA 1520 The problem is to find how large a fishpond can be equipped with a surround 2 flags wide, so that no pattern of 4 flags repeats itself when there are just 3 different colours of slabs.
• The curious case of the Chinese remainder theorem and its relation to RSA encryption
• A number consisting only of ones cannot be a perfect square Chris Petrie’s solution
• Planimeter by Chris Petrie text diagram
• ENIGMA 1507 Equal chance from New Scientist
• No π in the jar from Arthur Lupton — Robin’s answer — Arthur’s answer
• Dutch article about straight line drawing machine discovered by Robin Corbett.
• Another straight line drawing machine discovered by Robin Corbett.
• A puzzle posed on April Fool’s Day.
• ENIGMA 1487 Fermat plus 1 from New Scientist
• Can we justify this piece from Feedback from New Scientist?
• ENIGMA 1485 Fund Raiser − from New Scientist
• Robin Corbett’s straight line drawing machine
• The overhang problem from New Scientist
• Arthur Eddington’s Cricket problem — DH’s thoughts
• John Hughes’s Garden problem — Chis Petrie’s solution — Robin Corbett’s solution
• Chis Petrie’s “grandad” problem — DH’s thoughts — Robin’s much better thoughts

With the annual controversy about “dumbing down” of GCSE and A-level, it might be interesting to look at the maths School Certificate from 1941.
        Arithmetic         Geometry         Algebra                original papers courtesy of Ron Hudson

Recent GCSE papers are available from the AQA website.
Here are links to the PDF files for the three levels of June 2006 Paper 1:
        Foundation        Intermediate        Higher

I’ve looked back at New Scientist Enigma puzzles, and most of them seem to be trial-and-error computer problems, but here are some that might appeal:

• ENIGMA 1465 To the far quarter   —   DH’s partial answer
• ENIGMA 1450 Triangular dominoes
• ENIGMA 1452 Crossed lines   —   DH’s answer
• ENIGMA 1456 Cutting edge   —   DH’s answer
• ENIGMA 1457 Anglo-Italian sums

Puzzles from 2006/7 session:

• Arthur Lupton’s integer identities — DH’s thoughts — AL’s thoughts
• Arthur Lupton’s ray of sunshine.
• Leonardo da Vinci’s Bridge revisted.
• Hydro-Electricity for Settle (?) — Sterling work by John Hughes
• Hydro-Electricity for Settle (?) — DH’s initial effort
• Not Decimal — contributed by Chris Petree
  Under what circumstances is the following multiplication correct?
           14,300 × 43,211  =  32,213,100
• Leonardo da Vinci’s Bridges
  Do they really work? More information.
• Lagrange points
  New Scientist
  John Hughes’ contribution
  DH’s collaboration with Arthur Lupton
• ENIGMA 1373 From Point to Corner (DH’s answer.)
• Darts Where should a player aim to maximise the score
• Is a lead balloon possible? (DH’s thoughts on the subject.) (JMDH’s thoughts on the subject.)
• ENIGMA 1365 European Champions’ League (DH’s answer.)
• ENIGMA 1363 Hat Stand
• ENIGMA 1362 Eight-fifths DH’s answer
• ENIGMA 1352 Old MacDonald DH’s worst answer   DH’s best answer
• ENIGMA 1356 Magic spot
• ENIGMA 1358 Five fives
• Sudoku’s popularity surely deserves some attempt to investigate the phenomenon. (DH’s answer.)

• The Curious Incident of the Dog in the Night-time game show puzzle
• Fibonnaci as analysed by Arthur Lupton and by David Holdsworth
• ENIGMA 1205 Ever decreasing angles DH’s answer.
• Lewis Carrol’s Specious proof that all triangles are equilateral
• ENIGMA 1279 Big deal DH’s answer.
• ENIGMA 1190 Triple duel DH’s answer.
• ENIGMA 1322 Geometric Runs DH’s answer.
• ENIGMA 1314 Times Table
  Sorry but this has a typo, and I cannot find my copy of New Scientist.
• John Hughes’s baker problem DH’s answer using matrices
  I’ve not worked out how to put Robin’s answer in the web, but it agrees with mine.
• ENIGMA 1311 Geometry of the hands of a clock DH’s answer
• Arthur Lupton’s bishop problem look at DH’s DH’s proper answer. There is also DH’s DH’s partial answer to show how not to do it.
• ENIGMA 1313 Area of an Inner Triangle DH’s answer as corrected by Robin
• ENIGMA 1309 Board Game
• ENIGMA 1303 Alex and Monica’s code DH’s answer
• ENIGMA 1308 Passing through DH’s answer
• ENIGMA 1296 Embedded Triangles DH’s answer
• ENIGMA 1302 Luncheon meet looked at on 12^th October 2004 DH’s answer JMDH’s answer
• ENIGMA 1299 Pipes in a box looked at on 12^th October 2004 DH’s answer

To get DH’s SOMA cube program do the same kind of "save target as ..." on this link.