1. Douglas Fir tree rings - excavated from a cave in Arizona. Date: 577 ± 50 years AD

Answer: 1373

2. Wood from Egyptian coffin - from the Ptolemic period based on style. Date: 200 ± 150 years BCE

Answer: 2150

3. Wood fragments from the floor of a palace in Syria - Syro-Hittite period. Date: 675 ± 50 years BCE

Answer: 2625

4. Giant Sequoia tree rings from California. Date: 979 ± 52 years BCE

Answer: 2929
5. Cedar of Lebanon fragments from funeral boat of Egyptian King Sesostris III. Date: 1843 ± 50 years BC

Answer: 3793

6. Wood from the tombs of Egyptian Kings Sneferu and Zoser. Average Date: 2650 ± 75 years BCE

Answer: 4600

7. Wood from Bristlecone Pine of White Mountains, California. Age 4731 ± 75 years

Answer: 4682

8. Pleistocene mammoth bone from La Brea Tar Pits of Los Angeles, California. Age: 12,200 ± 35 years

Answer: 12151

9. Cottage roof timber from Ireland. Date: 906 ± 35 years

Answer: 857

857

10. Wood from the desk where Shakespeare wrote his plays. Date: 1610 ± 50 years

Answer: Well, that desk sure saw a lot of "bard" jokes! But in all seriousness, the date would be around 1560.

1. Douglas Fir tree rings from Arizona cave: The date of the tree rings is 577 ± 50 years AD. Subtracting the range (50 years) from the given date (577), we get the lower limit of the date: 577 - 50 = 527. Adding the range (50 years) to the given date (577), we get the upper limit of the date: 577 + 50 = 627. Therefore, the estimated date for the Douglas Fir tree rings is 527-627 AD.

2. Wood from Egyptian coffin: The date of the wood is 200 ± 150 years BCE. Subtracting the range (150 years) from the given date (200), we get the lower limit of the date: 200 - 150 = 50 BCE. Adding the range (150 years) to the given date (200), we get the upper limit of the date: 200 + 150 = 350 BCE. Therefore, the estimated date for the wood from the Egyptian coffin is 50-350 BCE.

3. Wood fragments from the floor of a palace in Syria: The date of the wood fragments is 675 ± 50 years BCE. Subtracting the range (50 years) from the given date (675), we get the lower limit of the date: 675 - 50 = 625 BCE. Adding the range (50 years) to the given date (675), we get the upper limit of the date: 675 + 50 = 725 BCE. Therefore, the estimated date for the wood fragments from the palace in Syria is 625-725 BCE.

4. Giant Sequoia tree rings from California: The date of the tree rings is 979 ± 52 years BCE. Subtracting the range (52 years) from the given date (979), we get the lower limit of the date: 979 - 52 = 927 BCE. Adding the range (52 years) to the given date (979), we get the upper limit of the date: 979 + 52 = 1031 BCE. Therefore, the estimated date for the Giant Sequoia tree rings from California is 927-1031 BCE.

5. Cedar of Lebanon fragments from funeral boat of Egyptian King Sesostris III: The date of the fragments is 1843 ± 50 years BC. Subtracting the range (50 years) from the given date (1843), we get the lower limit of the date: 1843 - 50 = 1793 BC. Adding the range (50 years) to the given date (1843), we get the upper limit of the date: 1843 + 50 = 1893 BC. Therefore, the estimated date for the Cedar of Lebanon fragments from the funeral boat of Egyptian King Sesostris III is 1793-1893 BC.

6. Wood from the tombs of Egyptian Kings Sneferu and Zoser: The average date of the wood is 2650 ± 75 years BCE. Subtracting the range (75 years) from the given date (2650), we get the lower limit of the date: 2650 - 75 = 2575 BCE. Adding the range (75 years) to the given date (2650), we get the upper limit of the date: 2650 + 75 = 2725 BCE. Therefore, the estimated date for the wood from the tombs of Egyptian Kings Sneferu and Zoser is 2575-2725 BCE.

7. Wood from Bristlecone Pine of White Mountains, California: The age of the wood is 4731 ± 75 years. Subtracting the range (75 years) from the given age (4731), we get the lower limit of the age: 4731 - 75 = 4656. Adding the range (75 years) to the given age (4731), we get the upper limit of the age: 4731 + 75 = 4806. Therefore, the estimated age for the wood from Bristlecone Pine of White Mountains, California is 4656-4806.

8. Pleistocene mammoth bone from La Brea Tar Pits of Los Angeles, California: The age of the bone is 12,200 ± 35 years. Subtracting the range (35 years) from the given age (12,200), we get the lower limit of the age: 12,200 - 35 = 12,165. Adding the range (35 years) to the given age (12,200), we get the upper limit of the age: 12,200 + 35 = 12,235. Therefore, the estimated age for the Pleistocene mammoth bone from La Brea Tar Pits of Los Angeles, California is 12,165-12,235.

9. Cottage roof timber from Ireland: The date of the timber is 906 ± 35 years. Subtracting the range (35 years) from the given date (906), we get the lower limit of the date: 906 - 35 = 871. Adding the range (35 years) to the given date (906), we get the upper limit of the date: 906 + 35 = 941. Therefore, the estimated date for the cottage roof timber from Ireland is 871-941.

To find the dates for these artifacts and wood samples, scientists use a method called dendrochronology, which involves analyzing tree rings. Here's a step-by-step guide on how to determine the dates:

Step 1: Collect samples
Scientists collect samples of wood from different sources and locations. In these examples, the samples include Douglas Fir tree rings, wood from an Egyptian coffin, wood fragments from a Syrian palace, giant Sequoia tree rings, Cedar of Lebanon fragments, wood from the tombs of Egyptian Kings Sneferu and Zoser, wood from Bristlecone Pine, Pleistocene mammoth bone, and cottage roof timber from Ireland.

Step 2: Analyze tree rings
The samples are carefully analyzed to identify the tree rings. Each ring corresponds to one year of growth for the tree. The rings vary in thickness, color, and density, depending on the environmental conditions during that year.

Step 3: Build a chronology
Scientists compare the tree rings from different samples to create a master chronology, which is a record of tree ring patterns for a particular region. This chronology provides a reference for dating purposes.

Step 4: Cross-matching
The master chronology is then cross-matched with the tree rings from the samples to identify matching patterns. By finding matching sequences of tree rings, scientists can determine the age of the samples.

Step 5: Calibration
To ensure accuracy, scientists use radiocarbon dating techniques to calibrate the tree ring dates. Radiocarbon dating involves measuring the amount of radioactive carbon in a sample, which can then be used to estimate its age.

Step 6: Calculate the dates
By cross-matching the tree ring patterns and calibrating using radiocarbon dating, scientists can calculate the approximate dates of the artifacts and wood samples.

Therefore, the estimated dates for the given examples are as follows:
1. Douglas Fir tree rings from Arizona cave - 577 ± 50 years AD = 1373
2. Wood from Egyptian coffin from the Ptolemaic period - 200 ± 150 years BCE = 2150
3. Wood fragments from the floor of a palace in Syria from the Syro-Hittite period - 675 ± 50 years BCE = 2625
4. Giant Sequoia tree rings from California - 979 ± 52 years BCE = 2929
5. Cedar of Lebanon fragments from funeral boat of Egyptian King Sesostris III - 1843 ± 50 years BCE = 3793
6. Wood from the tombs of Egyptian Kings Sneferu and Zoser (average date) - 2650 ± 75 years BCE = 4600
7. Wood from Bristlecone Pine of White Mountains, California - age 4731 ± 75 years = 4682
8. Pleistocene mammoth bone from La Brea Tar Pits of Los Angeles, California - age 12,200 ± 35 years = 12151
9. Cottage roof timber from Ireland - 906 ± 35 years = 857

Please note that these dates are approximations and are based on the scientific methods explained above.