Trick-or-Treat MathPro Problems > Math > Number and Quantity
Ned, Ted, and Jed go trick-or-treating on Halloween. They divide up their trick-or-treating territory into three regions, and each of the three friends cover a different region. They agree that when they meet up at the end of the evening, they'll divide up the loot evenly among the three of them.
When they meet, they find that they have the following totals:
3 Mars bars
22 Candy Corns
20 Candy Pumpkins
They agree that they should treat the candy corn as the "candy currency" - they are worth the same amount to each of them.
However, Ned says, "I think a Mars bar is worth 10 candy corns, and a candy pumpkin is worth 3 candy corns."
Ted says, "I think a Mars bar is worth 8 candy corns, and a candy pumpkin is worth 2 candy corns."
Jed says, "I think a Mars bar is worth 5 candy corns, and a candy pumpkin is worth 4 candy corns."
Can you help Ned, Ted, and Jed divide their loot in a way that satisfies all of them, without dividing any individual candies into parts?
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We'll call any sequence of letters a word, even if it isn't an English language word - for example, we'll call XWF a word, even though it has no meaning.
How many three-letter "words" are there that have a numerical value of 12?
A sheet of paper has two positive integers written on it. The two numbers add to 38. If neither integer is a one-digit number, and neither integer is even, what is the largest possible integer that could be written on the page?