The largest unmakeable total
A vending machine accepts only two chip denominations, worth 4 and 7 credits, and you may use any number of each (including none). Many totals — like 5 or 17 — cannot be paid exactly. What is the largest total (in credits) that cannot be formed as a non-negative combination of 4s and 7s?
Show hints (2)+
- Sort totals by their residue mod 4; within a class, adding 4s covers everything above the entry point.
- The entry point of each class is set by how many 7s you need to reach that residue.
Answer
Reveal answer →Final answer
17
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Asked at: Jane Street, Optiver