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Sum Equals Product

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Special Sums and Products

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Tweedle Dum and Tweedle Dee

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3
Tweedle Dum and Tweedle Dee

They were standing under a tree, each with an arm round the other's neck, and Alice knew which was which in a moment, because one of them had "DUM" embroidered on his collar, and the other "DEE."

"I suppose they've each got 'TWEEDLE' round at the back of the collar," she said to herself.

Two brothers were left some money, amounting to an exact number of pounds all in coins, to divide between them. DEE undertook the division.

"But your heap is larger than mine!" cried DUM.

"True," said DEE. "Allow me to present you with one-third of my heap."

DUM added it to his heap, and after looking thoughtfully at the now gigantic pyramid, he suddenly exclaimed "I am well off now! Here is half of the heap for you."

"You are generous," said DEE, as he swept up the money. "Two-thirds of this heap is the least I can offer you."

"I will not be outdone in generosity!" cried DUM, hastily handing over three-quarters of his property.

"Prudence is a virtue," remarked DEE. "Content yourself with two-thirds of my present wealth."

"One-third of mine is all I can now afford!" retorted DUM.

"And now, if I give you one pound," remarked DEE, "we shall, I think, be square?"

He was right. How much money was shared between them?