How to evaluate power towers?

Logic Level 3

$\Large 2 \; \underbrace{\square \; 2 \; \square \; \cdots \; \square \; 2 \; \square}_{n \text{ number of }\square\text{'s}} \; 2 = 2^{2^{2^{2^2}}}$

What is the minimum value of positive integer $n$ such that we can fill in the boxes above with the four mathematical operators ( $+, -, \times , \div$ ) and the equation holds true?

Note : Order of operations (BODMAS) applied.

Bonus : What would the answer be if we were to find the maximum value of integer $n$ ?

The answer is 65535.

1 solution

Alekhya China
Jul 11, 2016

among the operations +,-, ,/ the value can increase in the greatest rate by using * in all places now we need to calculate how many * in 2 2 2 ........*2=2^65536. so the no of * will be 65535. want explanation?

Want explanation? Yes

Pi Han Goh - 4 years, 11 months ago

it's very simple-if we evaluate the right hand tower then it becomes2^65536.hence in left hand side 65536 2's are to be multiplied.so the no of * signs are 65535.did you get it?

ALEKHYA CHINA - 4 years, 11 months ago

Yes! Yeeees! Thanks

Pi Han Goh - 4 years, 11 months ago

@Pi Han Goh – are you a Olympiad aspiarant mr.Pi Han Goh

ALEKHYA CHINA - 4 years, 11 months ago

@Alekhya China – haha, no no.

Pi Han Goh - 4 years, 11 months ago

@Pi Han Goh – can you tell me some good names of problem books of number theory ?

ALEKHYA CHINA - 4 years, 11 months ago

@Alekhya China – This one

Pi Han Goh - 4 years, 11 months ago

How to evaluate power towers?

The answer is 65535.

1 solution

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