Problem 4 · 2012 Math Kangaroo
Easy
Number Theory
mod-10divisibility
The positive whole numbers are being coloured in order, in red, blue and green, i.e. 1 red, 2 blue, 3 green, 4 red, 5 blue, 6 green, and so on. Which colour could the sum of a red number and a blue number be?
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Answer: C — green only
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Hint 1 of 2
Red, blue, green repeat every three numbers — look at remainders when dividing by 3.
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Hint 2 of 2
Add a 'red' remainder to a 'blue' remainder and see which colour the total lands on.
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Approach: track the colour by remainder mod 3
- Red numbers leave remainder 1, blue leave remainder 2, green leave remainder 0 when divided by 3.
- A red plus a blue gives remainder 1+2 = 3, i.e. remainder 0.
- Remainder 0 is exactly the green colour, so the sum is always green only.
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