Try this beautiful problem from Algebra about Largest and smallest numbers from AMC-8, 2006.
Largest and smallest numbers | AMC-8, 2006|Problem 22
Three different one-digit positive integers are placed in the bottom row of cells. Numbers in adjacent cells are added and the sum is placed in the cell above them. In the second row, continue the same process to obtain a number in the top cell. What is the difference between the largest and smallest numbers possible in the top cell?
- 34
- 12
- 26
Key Concepts
Number theory
Number counting
integer
Check the Answer
But try the problem first…
Answer:$26$
AMC-8, 2006 problem 22
Challenges and Thrills in Pre College Mathematics
Try with Hints
First hint
the lower cells contain A,B and C,
Can you now finish the problem ……….
Second Hint
the second row will contain A+B and B+C and the top cell will contain A+2B+C.
can you finish the problem……..
Final Step
If the lower cells contain A,B and C, then the second row will contain A+B and B+C and the top cell will contain A+2B+C. To obtain the smallest sum, place 1 in the center cell and 2 and 3 in the outer ones. The top number will be 7 . For the largest sum, place 9 in the center cell and 7 and 8 in the outer ones. This top number will be 33. The difference is 33-7=26
Other useful links
- https://www.cheenta.com/circles-and-semi-circles-amc-8-2010problem-23/
- https://www.youtube.com/watch?v=e2oyUpYCeBI
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