Problem solving activities for teenagers – Long String Guesses
Main aim: Find the length of each piece of string
Name: Long String Guesses
Type: Problem solving activities for teenagers
Participants: Individuals. This activity may be undertaken by a small group. Suitable for Middle School or Junior High (Years 7 and 8) students
Duration: 15-20 minutes
Materials: One piece of long string or rope at least 30 cm long (length of a ruler), scissors and stationery (pencil, eraser etc) for calculations
- Give each person (or group) the piece of string.
- Each person or group must cut a 2 cm piece off the string.
- Each person or group must then cut the string into another 4 pieces following these rules:
- each piece of cut string is a whole number of cm;
- none of the 5 pieces of cut string (including the first 2 cm piece) is of the same length; and
- none of the lengths is a multiple of any of the other lengths.
- The person or group must find out the shortest possible total combined length of the 5 pieces of cut string. There should be leftover string from the 30 cm original string.
- Note that the person or group should be warned that the remaining 4 pieces of cut string should not be cut until they are sure that they have solved the problem.
The length of each piece of cut string should be the first 5 prime numbers and the total combined length should be 28 cm.
The students or participants would have to work their way up the lengths in a systematic manner.