Study a touchtone phone's keypad, such as the one shown.
Suppose your phone number was 555-2362. Imagine you are entering this number, focusing on the last four digits. This number is called a "triangular phone number" because when entering the last four digits, your fingers trace a triangle.
For a telephone number to be "triangular," the first and last digits must be equal.
Question 1: How many different triangular phone numbers are there?
Note, you will have to decide what "different" means in your solution of the problem...
Question 2: Can you find two triangular phone numbers that are "similar" but not "congruent"?
- Do the telephone numbers ending in 2362, 2632, or 3623 form different triangles?
- Do the telephone numbers ending in 2362 and 5695 form different triangles?
Question 3: By now using the last digit from the initial 3-digit exchange, how many different quadrilateral phone numbers can you find?
How many are squares? Rectangles? Rhombuses? Parallelopgrams? Trapezoids?
Question 3: By now using the last two digits from the initial 3-digit exchange, how many different pentagonol phone numbers can you find?
If regular, then you have a "golden" pentagonal telephone number!
Source: Adapted from Michael Contino, CMC ComMuniCator, Vol. 17#3, p. 58
Hint: Produce and compare lists as you build them...trying to be systematic.
Solution Commentary: Sorry, no answer is being provided....I'm too busy calling my "square" friends!