Problem 4 · 2009 Math Kangaroo
Easy
Geometry & Measurement
careful-counting
In the picture you see the number 930. How many small squares must be changed so that the number becomes 806?
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Answer: B — 6
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Hint 1 of 3
Look at one digit at a time: the 9 changing to 8, the 3 changing to 0, and the 0 changing to 6.
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Hint 2 of 3
For each digit, lay the new shape on top of the old one and watch only the little squares that have to switch from dark to light or light to dark.
Still stuck? Show hint 3 →
Hint 3 of 3
Add up the switches from all three digits.
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Approach: compare the two numbers one digit at a time and count the little squares that flip
- Look at each digit on its own: 9 becomes 8, then 3 becomes 0, then 0 becomes 6.
- For the first digit, just one little square switches to turn the 9 into an 8.
- For the middle digit, two little squares switch to turn the 3 into a 0; for the last digit, three little squares switch to turn the 0 into a 6.
- Counting the switches: 1 + 2 + 3 = 6, so 6 small squares must be changed.
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