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Suppose that Geordie hires you as a consultant and asks you replace Combo 5 with a new Combo consisting of the same items (cookies, muffins, and so on), so that the organizers now have only one unique way of purchasing Combos to meet their requirements. Come up with such a Combo and show that it satisfies Geordie's condition. Your combo does not need to include every item, and can include as many or as few items of each item as you wish (though you may not use negative items). 2. Geordie's Café bundles together pastry and drink items in the following way: • Combo 1: One cookie, one muffin, and one coffee. • Combo 2: One muffin, one scone, and one coffee. • Combo 3: Three cookies; three donuts, and three coffees • Combo 4: One cookie, one muffin, one donut, one scone, and one coffee. • Combo 5: Two cookies, thrce muffins, one scone, and three coffees.

Answer :

One way to create a new Combo that satisfies Geordie's condition is to combine the items from Combo 1, Combo 2, and Combo 4.

This new Combo would consist of one cookie, one muffin, one scone, and one coffee.
To show that this Combo satisfies Geordie's condition, we can compare it to the original Combos:
Combo 1: One cookie, one muffin, and one coffee.
Combo 2: One muffin, one scone, and one coffee.
Combo 3: Three cookies, three donuts, and three coffees.
Combo 4: One cookie, one muffin, one donut, one scone, and one coffee.
Combo 5: Two cookies, three muffins, one scone, and three coffees.

By combining the items from Combo 1, Combo 2, and Combo 4, we have created a new Combo that includes one of each item: one cookie, one muffin, one scone, and one coffee.

This new Combo meets Geordie's requirement of having only one unique way of purchasing Combos because it is different from any of the original Combos. None of the original Combos have this exact combination of items.

In conclusion, by replacing Combo 5 with this new Combo, Geordie's condition is satisfied.

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