 ## ________________

Points and lines are the theme this week.

## ________________ Define a link as a straight line connecting any two points of the six points in the figure
to the right.

How many links can be placed without forming a triangle having three of the points
as vertices? ### Seven Points

Place seven points at different positions on the same plane so that for any three chosen, at least two will be exactly one foot apart.

## Solutions to week 132

The time in Time of Day is 8:24 am. The simple continuous function in The Missing Element is F(x) = 120(2x – 1)/x. The terms shown are for x = -3, -2, -1, 0, 1, 2, 3, 4, 5, 6. q = F(0) = 120 × ln2 which is approximately equal to 83.17766.

Time of Day answer explained:
For the hour hand to be exactly on a minute, the second hand must be on the 12. If the second hand is 18 minute marks ahead of the hour hand, the hour hand is on the 42nd minute mark and the time is 8:24. It must be 8:24 am because it would not be daylight at 8:24 pm.

The Missing Element answer explained:
The sequence can be expressed by the simple continuous function, F(x) = 120(2x – 1)/x when x is not equal to 0. The terms shown are for x = -3, -2, -1, 0, 1, 2, 3, 4, 5, 6. To get q, take the limit of F(x) as x approaches 0. When x is very near 0, 2x = exln2 ≈ 1 + xln2 where ln2 is the natural logarithm of 2 ≈ .6931472. This produces q = 120 × ln2 ≈ 83.17766.

## Recent Weeks

Links to all of the puzzles and solutions are on the Complete Varsity Math page.

Come back next week for answers and more puzzles.