perplexus.info :: Just Math : Getting gadgets galore

Getting gadgets galore (Posted on 2011-12-12)

To buy a certain gadget you need at least four US coins,- two similar gadgets require no less than six coins while for a purchase of three only two coins are needed.
What minimal price of the said item fits the description above?

Rem: The coins denominations are 1,5,10,25,50,100 cents .

No Solution Yet Submitted by Ady TZIDON

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

Makes cents (spoiler)

| Comment 1 of 3

Consider first buying 3 items with two coins. The two coins must sum to a multiple of 3, so the three must cost either 6, 15, 30, 51, 60, 75, 105 or 150 cents.

That makes one gadget either 2,5,10,17,20,25,35 or 50 cents.

Only 17 cents requires more than two coins, so that is our solution. It is not only minimal, it is unique.

Just as a check, two gadgets costs 34 cents, which requires at least 6 coins.

Posted by Steve Herman on 2011-12-12 11:13:09

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