Neurobics

Russell Dear

Digital Digits

On a calculator the digits 0 to 9 are represented by using some of seven possible line segments in a liquid crystal display. For example, the digits 1, 7 and 8 use two, four, and all seven line segments respectively:

Most 24-hour digital clocks show hours and minutes with a display which uses some of these 28 line segments:

(1) How many of the 28 line segments are not used?

(2) Which of the line segments is "on" more than any other?

(3) Which of the 21 line segments to the right is "on" for less time than any other?

(4) At what time are the least number of line segments used?

(5) At what time are most used?

Answers

(1) One
(2) The lower right-hand vertical segment in the furthest right batch of seven segments.
(3) The lower left-hand vertical segment of the second batch of seven segments from the right.
(4) If a zero is not placed in the left-hand "column" then 1:11, otherwise 11:11.
(5) 20.08

A Hard Day's Tramp

Kiri and Megan slumped down by the campfire after a hard day's tramping.

"I'm getting too old for this", sighed Megan.
"How old are you anyway?" asked Kiri.
"That would be telling," replied Megan, "but I'll give you a clue. My age is exactly divisible by both the sum and the product of its two digits, and, coincidentally, so is my son's."

How old is Megan?

Answer

There are only three two digit numbers that have this property and only the largest, 36, fits the information given in the problem. What are the other two numbers and how old was Megan's son?