Question 1 - Figure it out - Page 63, 64 - Chapter 3 Class 7 - Finding Common Ground (Ganita Prakash II)

Transcript

Question 1 In the two rows below, colours repeat as shown. When will the blue stars meet next?We can see that the stars repeat, like Repeats after 6 stars Repeats after 4 stars First Row Pattern: The colors repeat every 𝟔 stars (Yellow, Green, Orange, Blue, Purple, Grey). The Blue star is at position 4. Second Row Pattern: The colors repeat every 𝟒 stars (Green, Orange, Yellow, Blue). The Blue star is at position 4. Now, When both rows start together, blue stars meet at the 4th position So, next when both rows start together, blue star will meet at the 4th position after it And, Both rows start together at the Least Common Multiple (LCM) of their repeating patterns (6 and 4). Thus, we can write Blue stars meet next = 4 + LCM of 4 & 6 Finding LCM of 6 & 4 LCM of 4 & 6 = 2 × 2 × 3 = 12 The LCM is 12. This means the pattern aligns again every 12 stars. Thus, Blue stars meet next = 4 + LCM of 4 & 6 = 4 + 12 = 16 Thus, blue stars will meet next at the 16th star