A group of 20 students are sitting in a circle. Each shakes hands with exactly 3 neighbours. How many handshakes occur?
30
If every one of the \(n = 20\) students shakes hands with exactly \(d = 3\) others, then the sum of degrees is \(n \times d = 20 \times 3 = 60\).
Each handshake is counted twice in the degree sum (once for each participant), so the number of distinct handshakes is
\(\dfrac{n \times d}{2} = \dfrac{60}{2} = 30\).
Hence the correct answer is 30.
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Important Questions from Problem Solving
Evaluate 5793405 x 99999
A tight fitting band is wrapped around the Equator. Another circular band whose length is 15 m more lies at a certain height over the first band. A group of human beings attempt to pass under the longer band. Can they walk under it?
(Earth’s circumference is roughly 40000 km. The height of human beings is between 1 & 2m)
Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 - Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(84, 73, 157) (96, 88, 184)
- Arrange the problem-solving strategy.
(A) Generate many possible solutions
(B) Determine how to implement the solution and evaluate the success of the solution
(C) Make a decision
(D) Evaluate each solution
(E) Define the problem
Choose the correct answer from the options given below. People who are closest to information technology agree with the observation that benefits of screens as a learning tool are overblown and the risks for addiction and stunting development seems high. Screens are said to be beyond personal control and we situate them in pleasure centres of the developing brains. As a responsible parent you will
