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Class 6 Decomposition: Breaking Problems Down: cheat sheet
CBSE Computational Thinking and AI. Decomposition breaks a big problem into smaller parts that are easier to solve, then puts the answers together.
Key ideas
- Split a big task into sub-problems, solve each one, then combine them, like planning a picnic: place, food and transport.
- In a “Who am I?” puzzle, each clue removes the numbers that do not fit until only one is left.
- When things are passed between friends, the total they have together stays the same: a quick check on your working.
- For the fewest coins, use as many of the biggest coin as possible, then the next biggest, and so on.
- Comparison clues link into a chain: if A is taller than B and B is taller than C, then A is taller than C.
- Elimination crosses out what a clue rules out; often the last item left must be the answer.
Remember
| Fewest coins for ₹37 (₹10, ₹5, ₹2, ₹1) | 3 × ₹10 + 1 × ₹5 + 1 × ₹2 = 5 coins |
| Multiples of a up to N | whole part of N ÷ a |
| Multiples of a but not of b | multiples of a − multiples of both (both = multiples of the LCM) |
| Example | multiples of 4 but not 6 up to 60: 15 − 5 = 10 |
| Reading a table | find the row and the column together |
Watch out
- Reading the clues out of order, or skipping one, and ending with more than one answer.
- Changing only one person’s amount in a transfer: the giver loses what the receiver gains.
- Counting multiples of both numbers twice, or forgetting to take them away.
Worked example
(a) Priya, Zoya, Isha each have a different one of: guitar, drum, flute. Priya does not have the guitar. Isha has the guitar. Zoya does not have the drum. Who has the flute? (b) How many numbers from 1 to 70 are multiples of 5 but NOT multiples of 2?
Working: (a) only one way fits every clue: Priya – drum, Zoya – flute, Isha – guitar; (b) 14 multiples of 5, of which 7 are also multiples of 2 (multiples of 10)
Answer: (a) Zoya; (b) 7
Practise Decomposition: Breaking Problems Down
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