Question from the 2011 IMC key stage III paper, about determining which number has to be removed, so the...
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Question from the 2011 IMC key stage III paper, about determining which number has to be removed, so the multiplication is the square of an integer
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Question from the 2011 IMC key stage III paper, about determining which number has to be removed, so the multiplication is the square of an integer
Increasing sequence of divisors of a quadratic trinomialShow that $f(x)$ cant be written like thisIs every matrix product of this form?Squares and RationalizationShow that every integer eigenvalue of $A$ divides the determinant of $A$.Writing integers as a product of as few elements of ${frac21, frac32, frac43, frac54, ldots}$ as possibleFor which of the starting polynomials can Alice ensure that Bob does not win in finite number of moves?Does $A$ admit a square root with integer entries?Question from the 2011 IMC (International Mathematics Competition) Key Stage III paper, about the evaluation of a quadratic equationQuestion from the 2011 IMC (international mathematics competition) key stage III paper, about the evaluation of a+b+c
$begingroup$
The product $$1!cdot 2!cdot ldotscdot 2011!cdot 2012!$$ is written on the blackboard. Which factor in term of a factorial of an integer, should be erased so that the product of the remaining factors is the square of an integer?
I have absolutely no idea, as to how to solve, the question, above. Can you guys please help me?
linear-algebra logic contest-math problem-solving perfect-powers
edited 51 mins ago
greedoid
43.9k1155108
asked 1 hour ago
kenithkenith
474
$endgroup$
add a comment |
$begingroup$
The product $$1!cdot 2!cdot ldotscdot 2011!cdot 2012!$$ is written on the blackboard. Which factor in term of a factorial of an integer, should be erased so that the product of the remaining factors is the square of an integer?
I have absolutely no idea, as to how to solve, the question, above. Can you guys please help me?
linear-algebra logic contest-math problem-solving perfect-powers
edited 51 mins ago
greedoid
43.9k1155108
asked 1 hour ago
kenithkenith
474
$endgroup$
$begingroup$
So ONLY ONE number has to be removed?
$endgroup$
– Vinyl_coat_jawa
1 hour ago
$begingroup$
yes only one has to be removed
$endgroup$
– kenith
1 hour ago
add a comment |
$begingroup$
The product $$1!cdot 2!cdot ldotscdot 2011!cdot 2012!$$ is written on the blackboard. Which factor in term of a factorial of an integer, should be erased so that the product of the remaining factors is the square of an integer?
I have absolutely no idea, as to how to solve, the question, above. Can you guys please help me?
linear-algebra logic contest-math problem-solving perfect-powers
edited 51 mins ago
greedoid
43.9k1155108
asked 1 hour ago
kenithkenith
474
$endgroup$
The product $$1!cdot 2!cdot ldotscdot 2011!cdot 2012!$$ is written on the blackboard. Which factor in term of a factorial of an integer, should be erased so that the product of the remaining factors is the square of an integer?
I have absolutely no idea, as to how to solve, the question, above. Can you guys please help me?
linear-algebra logic contest-math problem-solving perfect-powers
linear-algebra logic contest-math problem-solving perfect-powers
edited 51 mins ago
greedoid
43.9k1155108
asked 1 hour ago
kenithkenith
474
edited 51 mins ago
greedoid
43.9k1155108
asked 1 hour ago
kenithkenith
474
edited 51 mins ago
greedoid
43.9k1155108
edited 51 mins ago
greedoid
43.9k1155108
edited 51 mins ago
greedoid
43.9k1155108
43.9k1155108
asked 1 hour ago
kenithkenith
474
asked 1 hour ago
kenithkenith
474
asked 1 hour ago
kenithkenith
474
474
$begingroup$
So ONLY ONE number has to be removed?
$endgroup$
– Vinyl_coat_jawa
1 hour ago
$begingroup$
yes only one has to be removed
$endgroup$
– kenith
1 hour ago
add a comment |
$begingroup$
So ONLY ONE number has to be removed?
$endgroup$
– Vinyl_coat_jawa
1 hour ago
$begingroup$
yes only one has to be removed
$endgroup$
– kenith
1 hour ago
$begingroup$
So ONLY ONE number has to be removed?
$endgroup$
– Vinyl_coat_jawa
1 hour ago
$begingroup$
So ONLY ONE number has to be removed?
$endgroup$
– Vinyl_coat_jawa
1 hour ago
$begingroup$
yes only one has to be removed
$endgroup$
– kenith
1 hour ago
$begingroup$
yes only one has to be removed
$endgroup$
– kenith
1 hour ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
So we have $$...=1!^23!^2...2009!^2cdot 2011!^2 cdot 2cdot 4cdot 6...cdot 2010cdot 2012$$
$$=1!^23!^2...2009!^2cdot 2011!^2 cdot 2^{1006}cdot color{red}{1006!}$$
answered 1 hour ago
greedoidgreedoid
43.9k1155108
$endgroup$
$begingroup$
thanks a lot mate
$endgroup$
– kenith
1 hour ago
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
So we have $$...=1!^23!^2...2009!^2cdot 2011!^2 cdot 2cdot 4cdot 6...cdot 2010cdot 2012$$
$$=1!^23!^2...2009!^2cdot 2011!^2 cdot 2^{1006}cdot color{red}{1006!}$$
answered 1 hour ago
greedoidgreedoid
43.9k1155108
$endgroup$
$begingroup$
thanks a lot mate
$endgroup$
– kenith
1 hour ago
add a comment |
$begingroup$
So we have $$...=1!^23!^2...2009!^2cdot 2011!^2 cdot 2cdot 4cdot 6...cdot 2010cdot 2012$$
$$=1!^23!^2...2009!^2cdot 2011!^2 cdot 2^{1006}cdot color{red}{1006!}$$
answered 1 hour ago
greedoidgreedoid
43.9k1155108
$endgroup$
$begingroup$
thanks a lot mate
$endgroup$
– kenith
1 hour ago
add a comment |
$begingroup$
So we have $$...=1!^23!^2...2009!^2cdot 2011!^2 cdot 2cdot 4cdot 6...cdot 2010cdot 2012$$
$$=1!^23!^2...2009!^2cdot 2011!^2 cdot 2^{1006}cdot color{red}{1006!}$$
answered 1 hour ago
greedoidgreedoid
43.9k1155108
$endgroup$
So we have $$...=1!^23!^2...2009!^2cdot 2011!^2 cdot 2cdot 4cdot 6...cdot 2010cdot 2012$$
$$=1!^23!^2...2009!^2cdot 2011!^2 cdot 2^{1006}cdot color{red}{1006!}$$
answered 1 hour ago
greedoidgreedoid
43.9k1155108
edited 1 hour ago
answered 1 hour ago
greedoidgreedoid
43.9k1155108
answered 1 hour ago
greedoidgreedoid
43.9k1155108
answered 1 hour ago
greedoidgreedoid
43.9k1155108
43.9k1155108
$begingroup$
thanks a lot mate
$endgroup$
– kenith
1 hour ago
add a comment |
$begingroup$
thanks a lot mate
$endgroup$
– kenith
1 hour ago
$begingroup$
thanks a lot mate
$endgroup$
– kenith
1 hour ago
$begingroup$
thanks a lot mate
$endgroup$
– kenith
1 hour ago
add a comment |
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$begingroup$
So ONLY ONE number has to be removed?
$endgroup$
– Vinyl_coat_jawa
1 hour ago
$begingroup$
yes only one has to be removed
$endgroup$
– kenith
1 hour ago