Mathematics · the experiment
Pin down the Frobenius number
Some amounts can never be paid exactly. Track down the largest, set it against the three bounds, then build a set of coins that hits the new one yourself.
1 · Find the last impossible amount
Beginner
3 and 6 share the factor 3. Why are the coins 3, 4 and 6 still allowed?
With coins of 3, 4 and 6, find the largest amount you cannot pay.
2 · Set the bound against the true F
Intermediate
Coins of 5, 6 and 10. What does the new bound aₙ₋₁⌈aₙ/(n − 1)⌉ − aₙ − 1 give?
With coins of 5, 6 and 10, find the largest amount you cannot pay.
3 · Hit the bound
Expert
In the family q, q + 1, 2q, why does the 2q coin change nothing about F?
Set three different coins, from 2 to 15, so that F equals the new bound exactly, with a set other than 3-4-6 and 5-6-10.
4 · Set a coin aside
Coins of 3, 40 and 50: the new bound gives 949. The authors allow you to set a coin aside, as long as the remaining coins have no factor common to all of them.
Expert
Which coin should you set aside to get a much lower bound?
Frobenius pinned down
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