Leigh & District

Maths

Hi, everyone,
Hope you are all coping well with the enforced isolation. A few days have been long and lonely but, in the main, I’m keeping busy.

I write this as an invitation to all, whether in the maths group or not, to join in with us doing a few maths based puzzles. You can do any which interest you and ignore the rest. You might even have a puzzle to offer yourself.

To join in just send your name by email to me at patriciatodd@live.co.uk and I shall put you on the mailing list. You will have no OBLIGATION to join the maths group when we are back to normal, but I shall be very pleased if you do.

The aim is to jiggle a few brain cells and to fill a moment (with a cup of coffee?)

Keep safe and well, Pat

Maths Puzzles

While we are unable to meet in person, I have some Maths puzzles that you may be interested in. See explanations below and associated links on the right.

Curves from Lines - There is a circle with numbered points and also a list of which points to join (each with a STRAIGHT line). Ideally you need to print off the circle, but if you have no printer the points are every 10 degrees on your protractor. This one is suitable for younger members of your family to try. They will be surprised at the finished result and if you never did “curve stitching” at school it may surprise you, too.

Mystic Circles - This puzzle I like because you can approach it from at least two directions and still come up with the correct answers.

• Starting with points on the circumference of a circle (preferably evenly spaced for beauty) each point is joined to ALL other points. Each is a CHORD of the circle. (A diameter is a special chord which happens to go through the centre.) Your job is to find out how many chords are needed to complete each.
• PLEASE, if you’re still drawing and counting chords after the 8 or 9 point circle look at your answers so far and see if there isn’t another way of getting the remaining numbers without any drawing at all (or I might be accused of cruelty and asked to leave the U3A).
• Email me with your answers, even if you only do the first 7 of them. Hints available if you want them.
• When you have filled the table you might want to have a go at the “n” part of the question but only if you LIKE algebra.
• The second page is a beautifully drawn 19 point Mystic Rose. Look closely and you will see concentric circles but it was drawn with only STRAIGHT lines.

One to Nine - This puzzle is quite straightforward but the examples get increasingly difficult. Feel free to answer as few as you like or even ask for additional clues to answer them all. Each one needs you to fit 1 to 9 in spaces to make an addition sum correct.

Number Box - The explanation is in the puzzle.

Ages - Here is a puzzle to get you thinking. It is adapted from a puzzle by the American, Sam Loyd, about 1900. There is no logic to the context of the question, it is contrived as an excuse to do some mathematical thinking. You must expect many of the characters’ ages to include fractions.

• As a child I went to Sunday school, but there were only 2 of us in the class, myself and a toddler, so the teacher hatched a plan to encourage more to enrol. She decided to offer a weekly prize to the boys or the girls, whichever had the greatest total age.
• The first week I got the prize because my age was twice that of the toddler.
• However, the next week she came with her sister to Sunday School and their combined ages were just twice mine, so the girls shared the prize.
• Two can play at that game. The next week I brought my brother and our combined ages were exactly twice as much as the combined ages of the two girls, so we took the honours and divided the prize between us.
• The battle continued. On the 4th Sunday the 2 girls were accompanied by an older cousin on what happened to be her 21st birthday: this time the 3 girls shared the prize because their combined ages were twice those of the combined ages of my brother and I.
• How old was I at the time?

Triangles - The instructions are in the puzzle.