Problem 11 · 2025 Math Kangaroo
Medium
Counting & Probability
careful-counting
Alex threads white and black beads alternately onto a piece of string. Twice, 5 beads are hidden — see picture. How many white beads are hidden in total?
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Answer: C — 6
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Hint 1 of 3
The beads always go white, black, white, black — never two of the same colour together.
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Hint 2 of 3
Look at the visible bead right before each hidden part to know what colour comes next.
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Hint 3 of 3
Fill in each hidden run of 5 by carrying on the colours, then count just the white ones.
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Approach: carry on the alternating colour pattern through each hidden run
- The beads keep switching: white, black, white, black, and so on.
- Each hidden group of 5 carries on that pattern, and in each one 3 of the 5 beads come out white.
- There are two hidden groups, so 3 and 3 make 6 white beads in total. The answer is C.
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