Problem 14 · 2014 Math Kangaroo
Medium
Counting & Probability
careful-counting
Gerhard has the same number of white, grey and black counters. He has thrown some of these round pieces together onto a pile. All the pieces he used can be seen in the picture. He has, however, got 5 counters left that will not stay on the pile. How many black counters did he have to begin with?
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Answer: B — 6
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Hint 1 of 3
He began with the same number of white, grey and black, so think of them in equal groups.
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Hint 2 of 3
Count the counters on the pile, colour by colour, from the picture.
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Hint 3 of 3
The 5 left over are the extras that did not fit, so add them back to find each starting group.
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Approach: count the pile by colour, then add back the leftovers to make equal groups
- Count how many white, grey and black counters are actually on the pile in the picture.
- He started with the same number of each colour, and 5 counters were left over that did not stay on.
- Sharing everything back into three equal colour groups, each group had 6 counters.
- So he began with 6 black counters.
Mark:
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