Enigma 1057: Recycled change
18 June 2018
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From New Scientist #2213, 20th November 1999 [link]
The denominations of coins currently in circulation are 200, 100, 50, 20, 10, 5, 2 and 1p. When we pay for an item we quite often exchange fewer coins when change is given than when the exact amount is offered. For instance, an item costing 91p would require at least four coins (50+20+20+1) for the exact amount, but the purchase can be made with the exchange of only three coins (100+1–10) if change is given.
Harry, Tom and I each bought an identical item that cost less than 100p. None of us offered the exact amount, but we each exchanged fewer coins than if we had done so. In fact, we each exchanged the minimum number of coins possible for an item of that price even though we each offered a different amount of money in payment.
I paid first, and Harry and Tom each included a different one of the coins I had received in my change among the coins that they offered.
How much did the item cost?