**4.1.** The Rhind papyrus is an ancient Egyptian mathematical manuscript that is more than 3500 years old. Problem 79 of the Rhind papyrus poses a problem that can be paraphrased as follows: there are seven houses; in each house lives seven cats; each cat kills seven mice; each mouse has eaten seven spelt seeds²³; each spelt seed would have produced seven hekat²⁴ of spelt. What is the sum of all of the named items? Solve this 3500 year old problem.

The Rhind papyrus is an ancient Egyptian mathematical manuscript that is more than 3500 years…

Answered: 4.1. The Rhind papyrus is an ancient…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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planet utopia, Utopians likely do not use decimal numbers. After playing with the calculator for a Problem 1.2: utopia number system You have found a calculator from the planet Utopia. You do not know the number system used on while, you have observed the following: a2 = a a+a=B 82 = BB 8+ 8 = aa a) What is the decimal value of a, B, and y? b) What is the decimal value of 6? What is the base used by the number system? c) How is the decimal number 99 written on planet Utopia?
Problem 9 How many possible passwords can be formed from the letters: ASSISTANT_TITAN ? How many different strings can be made from the letters in MISSISSIPPI, using all the letters? How many different strings can be made from the letters in ABRACADABRA, using all the letters? а. b. с.
Problem 10. Pigeonhole principle applications. Be sure to justify your answer. 10(d) There are 14 3-digit numbers in a list. Can you conclude that there are two distinct subsets of the 14 numbers that have the same sum?
PROBLEM 4 Solve the following problems: (a) How many ways can a store manager arrange a group of 1 team leader and 3 team workers from his 25 employees? (b) A state's license plate has 7 characters. Each character can be a capital letter (A – Z), or a non-zero digit (1 – 9). How many license plates start with 3 capital letters and end with 4 digits with no letter or digit repeated? (c) How many binary strings of length 5 have at least 2 adjacent bits that are the same ("00" or "11") somewhere in the string?
DISCRETE MATH problem
Problem 9 There are 51 houses on a street. Each house has an address between 1000 and 1099, inclusive. Show that at least two houses have addresses that are consecutive integers. K
Problem 5.4 (Grade a "Proof"). Study the following claim as well as the "proof": Claim. For all n e N, 3| (n³ +44n). “Proof". When n = 1, n³ +44n = 45 is divisible by 3. When n = 2, n³ +44n = 96 is divisible by 3. When n = 3, n³ + 44n = 159 is divisible by 3. When n = 100, n3 + 44n = 1004400 is divisible by 3. Thus 3 | (n³ +44n) for all n e N. %3D Complete the following questions concerning the above claim and "proof": (1) Determine whether the "proof" is rigorous. Identify the issues in the "proof", if any. (2) Determine whether the claim is true or false. Justify the answer in part (3). (3) If the the claim is true and the “proof" is not rigorous, then provide a correct and rigorous proof. If the claim is false, give a concrete counterexample. Hint. Complete the parts as instructed. If the claim is false, then (obviously) there is no way the "proof" could be correct.
Problem 1. How many words can be made by rearranging aabbccdd, such that no 'a' appears somewhere to the right of some 'c'? Justify your answer Problem 2 A

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