$x?$

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One day, my friend, Tict Hoong was imprisoned by an evil monster. The evil monster said that he is dull with those stupid factorials that I've learnt sometime ago, so he decided to change the exclamation mark to a question mark. Then, he said, 'This notation has a different meaning with that exclamation mark which is used to represent the factorial of a number.' He drank a cup of 'potion' and continues, 'Let $x$ be a positive number. If $x$ is odd then $x?$ will be the product of all the positive odd numbers that is smaller or equal to $x$ . If $x$ is even then $x?$ will be the product of all the positive even numbers that is smaller or equal to $x$ . Now, do you want to save your friend?' I replied, 'Yes,yes,yes..., of course!' After he had hesitated a little, he continues,'Okay, to save your friend, answer this: if $x?=135135$ and $y?=645120$ , find the number of guesses that I will be giving you if it is equal to $x+y$ . Remember, if you are run out of guesses, your friend will be my meal!' I got extremely anxious, and I had no idea on how to answer it. Can anyone please be kind to help me to solve this and save my friend?

The answer is 27.

1 solution

Ng Donn
Jan 22, 2014

$135135$ = $3^{3}$ x $5$ x $7$ x $11$ x $13$ = $1$ x $3$ x $5$ x $7$ x $9$ x $11$ x $13$ = $13?$

$645120$ = $2^{11}$ x $3^{12}$ x $5$ x $7$ = $2$ x $4$ x $6$ x $8$ x $10$ x $12$ x $14$ = $14?$

$x+y=13+14=27$

wow. OBVIOUS typo mistake! (Correction at Line 2: $3^{12}\implies 3^2$ )

敬全钟 - 7 years, 4 months ago

x ? x? x ?

The answer is 27.

1 solution

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$x?$