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Baltic Way 1992 · Problem 7

Algebra

Let a=19921992a=\sqrt[1992]{1992}. Which number is greater:

aa⋅⋅a⏟1992 copies of a\underbrace{a^{a^{\cdot^{\cdot^a}}}}_{1992\text{ copies of }a}

or 19921992?

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Topics

Sequences and recurrences · Algebraic manipulation

Solutions

Solution

Solution: The first of these numbers is less than the power tower obtained by replacing its topmost aa by 19921992. Since a1992=1992a^{1992}=1992, evaluating that larger tower from the top down gives 19921992 at every successive level. Hence the larger tower equals 19921992, so the first number is less than 19921992.

Contest context

Results from Baltic Way 1992

8 teams

Mean score
3.8 / 5
Scores of 4 or 5
6 / 8
Estonia
0 / 5

Score distribution

02
10
20
30
40
56
All team scores
TeamScore
Denmark5 / 5
St. Petersburg5 / 5
Poland5 / 5
Latvia5 / 5
Iceland0 / 5
Lithuania5 / 5
Estonia0 / 5
Sweden5 / 5