137
Solving logic problems
Textbook: Part 4, lesson 137, pp. 84–86
GoalLogic problems: forming numbers from digits, reasoning with sets, true and false statements.
New words
logic · mantiqdigits · raqamlarare not repeated · takrorlanmaydicondition · shart
Explanation
In a logic problem we check the conditions one by one and cross out impossible answers. When forming numbers from digits we write all the options in order: first the first digit, then the second. If we are told that only one of the statements is true, we try each option and count how many statements come out true.
Worked examples
Three-digit numbers from the digits 3, 5, 7 (no repeats): 357, 375, 537, 573, 735, 753 – 6 numbers. The largest is 753 and the smallest is 357.
4 of Zilola’s friends go to drawing and 5 go to singing. She can have 7 friends (2 go to both: 4 + 5 − 2 = 7), but not 3: 5 friends go to singing.
Class activity
“Logic club”: groups get a logic puzzle card, write the solution and explain it at the board. They must say which condition crossed out which answer.
Practice
1
How many three-digit numbers can be made from the digits 2, 6, 9 with no repeated digits?
6
2
4 of Aziza’s friends go to drawing, 5 go to singing and 3 go to both. How many friends does Aziza have?
6
3
An apple is in one of three boxes. Box 1 says “The apple is in this box”, box 2 says “The apple is not in box 1”, box 3 says “The apple is not in this box”. Only one label is true. Which box has the apple?
In box 3: then only label 2 is true. If it were in box 1 or box 2, two labels would be true.
4
The number is two-digit, a multiple of 7, and its digits add up to 5. Which number is it?
14
5
Ali, Vali and Sami took places 1, 2 and 3. Vali was not first or third. Ali finished before Sami. Who took which place?
Ali – 1st, Vali – 2nd, Sami – 3rd.