Why are they primes?

Logic Level 4

$2 \div 3\div 5 \div 7 \div 11 \div 13 \div 17 \div 19$

The value of the expression above is equal to $\dfrac{2}{4849845}$ .

If I added a pair of parentheses like $2 \div 3\div 5 \div 7 \div 11 \div 13 \div (17 \div 19) ,$ the resultant number will not be the same as the original number.

If I'm allowed to add any number of parentheses to the original expression above, how many distinct values can the resultant number take?

The answer is 64.

1 solution

Akhash Raja Raam
Feb 13, 2016

You need to just square the number of prime numbers. This is similar to "Find number of squares in the image" type of problems.

PS : If you find any mistake please correct me!

You need to just square the number of prime numbers.

Why is this true?

Pi Han Goh - 5 years, 4 months ago

I just squared 8 = 64 and that was the answer. I derived 8 from the number of primes in the question. I had studied it in my older school days when an absolutely big brained teacher taught me this formula. I just need to search for it. When I get it, I will post it here!

Akhash Raja Raam - 5 years, 3 months ago

Why are they primes?

The answer is 64.

1 solution

0 pending reports