For all Harry Potter Fans

Number Theory Level 4

\(\mathfrak{Harry Potter}\), you don't ask who, is now a grown up. To remember his old days, when he was young, he makes a visit to the Diagon Alley, with his friends, you don't ask whom.

Firstly, he visits the Ollivanders, Makers of Fine Wands since 382 BC, at the southern end of the Alley, where he buys a new "Taking Care of Your Wand" kit.

Then he takes the triple decker Knight Bus, which takes it to the northern end for more shopping. He goes to the Flourish & Blotts, and buys Gadding with Ghouls at a discounted price.

Then he goes to Madam Malkin's Robes for All Occasions, left of the Flourish & Blotts, to buy a brand new traveling cloak for himself.

After a day of hectic shopping, Harry goes to the Florean Fortescue's Ice Cream Parlour Redisigned, which was reinovated after the death of the owner Florean Fortescue.

As per the new rules, which Harry seemed to like lesser, the complete payment was to be done at the Gringotts Wizarding Bank, owned and operated by goblins.

Here, he finds a Goblin Griphook, who throws light upon his day's expenses, in Galleons.

Griphook: Sir, you have to pay 7.11 Galleons for the day.

Harry: How so?

Griphook: Sir, as per our impeccable records, you have purchased from our registered shops, a Taking Care of Your Wand kit, a copy of Gadding with Ghouls, a Traveling Cloak, and chocolate and raspberry ice cream with chopped nuts, large size.... and the product of all your individual expenses comes out to be 7.11

Harry: What?! Have you lost your wands? You were supposed to add them, were you not?

Griphook: Yes, most respected Sir, I was, but that doesn't really make much of a difference though.

Given that the travelling cloak was the most costly expense of Harry, how many Nuts should he have paid for it?

Details & Assumptions

\(\bullet\) Harry need not pay for the Knight bus.

\(\bullet\) A lot of care has been taken that the facts mentioned in the problem are error free, and any improvement in this regard is welcome.

\(\bullet\) All purchases were done in Galleons, in the IWU of Currency, where each Galleon is worth 10 Sickels, each worth, further, 10 Nuts. In the original Wizarding World is followed the SWU, where each Galleon is 17 Sickles, each worth 29 Knuts.


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