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Logic problems
Textbook: Part 4, pp. 101–103
GoalLogic problems: a number trick, measuring liquids, logical matching, forming numbers from digits, weighing with a balance.
New words
logic · mantiqguess · taxminchecking · tekshirishoption · variant
Explanation
We do not hurry in a logic problem: first we read the condition carefully, then we try the options in order and cross out the impossible ones. We always check the answer against the condition. A number trick reveals its secret when we write it step by step with numbers.
Worked examples
Trick: think of a number, double it, add 10, halve it, subtract the number you thought of – the answer is always 5. For 7: 14, 24, 12, 12 − 7 = 5. For 20: 40, 50, 25, 25 − 20 = 5.
To measure 4 l with a 5 l and a 3 l container: fill the 5 l one and pour into the 3 l one (2 l are left in the 5 l); empty the 3 l one and pour the 2 l into it; refill the 5 l one and top the 3 l one up with 1 l – 4 l are left in the 5 l container.
Class activity
“Logic contest”: groups solve puzzle cards. Each group explains its solution and another group looks for a mistake. The group with the clearest explanation wins.
Practice
1
Check the trick with the number 12: double it, add 10, halve it, subtract 12. What do you get?
5
2
You have a balance scale. One of 9 coins is heavier than the others. What is the smallest number of weighings that is sure to find it?
2: first compare 3 + 3, then compare 1 + 1 from the heavier group of three.
3
Sardor, Akmal and Jasur each do one of chess, football and swimming. Sardor does not play chess and does not swim. Akmal does not play football. Jasur does not swim. Who does what?
Sardor – football, Jasur – chess, Akmal – swimming.
4
How many three-digit numbers can be made from the digits 0, 4, 6 with no repeats? (A number cannot start with 0.)
4
5
A class has 24 children and each likes jumping or running. 16 like jumping and 14 like running. How many children like both?
6