FILE No.182Unsolved
A gang of robbers tried to split bundles of cash evenly. Dividing evenly among 7 people leaves them 2 bundles short. After some left and there were 5 people, they were still 2 bundles short, and with 3 people they were again 2 bundles short.
What is the smallest possible number of bundles?
If you get stuck, open the hints one at a time, in order.
What does "2 short" mean in terms of adding 2 bundles?
Think about numbers divisible by 7, 5, and 3.
What is the smallest such number?
What is the smallest possible number of bundles?
Choose the answer closest to the truth.
103 bundles
The answer is "103 bundles."
"2 bundles short" means "with 2 more bundles, it would divide evenly." The smallest number divisible by 7, 5, and 3 is 7 × 5 × 3 = 105. Subtracting 2 gives 103 bundles, which meets the conditions.
105 bundles would divide evenly, so it would not be "short." 98 is divisible by 7, but it is not "2 short" for 5 (98 + 2 = 100 is not divisible by 7).
Because it is easy to mistake "2 short" for "a remainder of 2."
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