I am just going to add some puzzles/problems each week and see if you people, in the world of Dp actually are really smart.
1. There are seven houses each containing 7 cats. Each cat kills 7 mice and each mouse would have eaten 7 ears of spelt.
Each ear of spelt would have produced 7 hekats of grain. What is the total of all of these?
2. Seven old women are travelling to Rome, and each has seven mules. On each mule there are seven sacks, in each sack there are seven loafs of bread, in each loaf of bread there are seven knifes, and each knife has seven sheaths. The question is to find the total of all of them. Solved by nightryder with the answer of 137,256
3. The St Ives Riddle
As i was going to St Ives,
I met a man with seven wifes.
Every wife had seven sacks,
Every sack had seven cats,
Every cat had seven kits;
Kits, cats, sacks and wifes,
How many were going to St Ives? Solved by Herron. With the answer of 1.
4. The greedy algorithm does not work so well if we add the condition that all the denominators must be odd. There are just five ways to represent 1 as the sum of the smallest possible number of Egyptian fractions, with odd denominators. Which has the smallest largest denominator?
5. What is the smallest fraction 3/n for which the greedy algorithm produces a sum in three terms, but two terms are actually the same? Seems theres something missing sorry.
6. How can 1/2 be represented as the sum of unit fractions with square denominators, with no denominator greater than 35 squared?
7. Problem 29 of the rhind papyrus is not so clear, but it is plausibly the first ever 'Think of a number' problem. It reads, 'Two-thirds is to be added. One third is to be subtracted. There remains 10'. In clearer language that reads: 'I think of a number, and add to it two-thirds of the number. I then subtract one-third of the sum. My answer is 10.' What number did i think of?
8. 'If the scribe says to thee, '10 has become 2/3 + 1/10 of what?' is the Egyptian way of saying, in effect, ' I think of a number. Two thirds of the number plus its tenth make 10.' What was that number?
If any of these don't make sense to you, then don't go asking me. I am dumb and explaining these would just confuse me and you.
Also i got these out of a book.
