Subtracting to 2008
Can you work out the sum of the missing digits in this subtraction?
In this subtraction, $P$, $Q$, $R$ and $S$ are digits. What is the value of $P + Q + R + S\;$?
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If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Answer: P + Q + R + S = 16
Subtracting
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![Subtracting to 2008 Subtracting to 2008](/sites/default/files/styles/large/public/thumbnails/content-id-10150-subtracting%252520to%2525202008%252520subtracting%2525201.png?itok=YYcBQ_VC)
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![Subtracting to 2008 Subtracting to 2008](/sites/default/files/styles/large/public/thumbnails/content-id-10150-subtracting%252520to%2525202008%252520subtracting%2525202.png?itok=Tf1oH7BO)
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![Subtracting to 2008 Subtracting to 2008](/sites/default/files/styles/large/public/thumbnails/content-id-10150-subtracting%252520to%2525202008%252520subtracting%2525203.png?itok=jfFRXqhO)
0 + 1 + 9 + 6 = 16
Adding
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![Subtracting to 2008 Subtracting to 2008](/sites/default/files/styles/large/public/thumbnails/content-id-10150-subtracting%252520to%2525202008%252520adding%2525201.png?itok=Nt_Nmx2b)
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![Subtracting to 2008 Subtracting to 2008](/sites/default/files/styles/large/public/thumbnails/content-id-10150-subtracting%252520to%2525202008%252520adding%2525202.png?itok=py0zFEE1)
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![Subtracting to 2008 Subtracting to 2008](/sites/default/files/styles/large/public/thumbnails/content-id-10150-subtracting%252520to%2525202008%252520adding%2525203.png?itok=9ErwDjF_)
so R+1 = 10 ie. R = 9, Q = 1 and P = 6, S = 0
9 + 1 + 6 + 0 = 16