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Logic Level 2

A ​ countdown number​ is a positive integer where the sum of each pair of consecutive digits forms part of a countdown. For example: 23120 is a countdown number because

2 , 3 , 1 , 2 , 0 2 + 3 = 5 2 , 3 , 1 , 2 , 0 3 + 1 = 4 2 , 3 , 1 , 2 , 0 1 + 2 = 3 2 , 3 , 1 , 2 , 0 2 + 3 = 2 \begin{aligned} &\boxed{2, 3}, 1, 2, 0 \longrightarrow 2 + 3 = \mathbf{5} \\ &2, \boxed{3, 1}, 2, 0 \longrightarrow 3 + 1 = \mathbf{4} \\ &2, 3, \boxed{1, 2}, 0 \longrightarrow 1 + 2 = \mathbf{3} \\ &2, 3, 1, \boxed{2, 0} \longrightarrow 2 + 3 = \mathbf{2} \\ \end{aligned}

What is the largest six-digit countdown number?


The answer is 998877.

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1 solution

Collin Lloyd
Nov 15, 2015

998877.

  • 9+9=18
  • 9+8=17
  • 8+8=16
  • 8+7=15
  • 7+7=14
  • Process for finding the solution: Knowing that the highest value single-digit number is 9, and therefore having known that the highest possible number that can be found by adding two single-digit numbers together is 18, it was just a process of subtracting 1 from the sum, then subtracting the number last used in the sequence to find the next number in the sequence.
  • Example: 18-1=17, last number in sequence so far = 9, 17-9=8. 17-1=16, last number in sequence so far = 8, 16-8=8.

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