Solve the given word problem: Selecting 2 numbers from a watch face

In summary, the problem involves selecting 2 numbers from a watch face, which consists of the numbers 1 through 12. The task is to determine the number of unique combinations of these two numbers, taking into account the circular arrangement of the watch face. This requires understanding combinatorial principles to ensure that selections are counted correctly without regard to order.
  • #1
chwala
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Homework Statement
see attached
Relevant Equations
grade 9 maths
I honestly do not understand this question, my thoughts;

ignoring the diagram and using algebra i can see that the step size [1,5] → [2,6] can be found by adding 1 (common difference) to each number meaning that the answer is A...

...the other options B,C,D and E can not be related by a common difference

1712715664990.png
 
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  • #2
Right now, 1 and 5 are shown.
After the disk is rotated, either
10 and X will show or
10 and Y will show.
But in both cases, the gap between 10 and the other (X or Y) will be the same as the gap between 1 and 5.
 
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  • #3
.Scott said:
Right now, 1 and 5 are shown.
After the disk is rotated, either
10 and X will show or
10 and Y will show.
But in both cases, the gap between 10 and the other (X or Y) will be the same as the gap between 1 and 5.
Aaaaaah haha... I can now see it ... the other number is either ##10+4= 2## or ##20-4=6##. The word problem was a bit confusing to me.
 
  • #4
chwala said:
or 20−4=6.
or 10-4=6.
 
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  • #5
Gavran said:
or 10-4=6.
yeah typo error. Cheers man.
 
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FAQ: Solve the given word problem: Selecting 2 numbers from a watch face

What does it mean to select 2 numbers from a watch face?

Selecting 2 numbers from a watch face typically refers to choosing any two distinct hour markers (numbers) on a standard 12-hour analog clock. The numbers range from 1 to 12, and the selection can be for various purposes, such as calculating angles, determining time intervals, or solving mathematical problems.

How many different combinations of 2 numbers can be selected from a watch face?

You can calculate the number of combinations of 2 numbers from 12 using the combination formula, which is C(n, k) = n! / (k!(n-k)!). Here, n is 12 (the total numbers on the watch face), and k is 2 (the numbers being selected). The calculation gives C(12, 2) = 12! / (2!(12-2)!) = 66 different combinations.

Are the order of selection and repetition allowed when choosing the numbers?

What are some examples of problems that can be solved by selecting 2 numbers from a watch face?

Examples include calculating the angle between the two selected numbers, determining the time interval between them, or creating a mathematical expression involving those numbers. These problems can be useful in geometry, time management, and number theory.

How can I visualize the selection of numbers on a watch face?

You can visualize the selection by imagining a circular clock where the numbers 1 through 12 are evenly spaced around the circle. When selecting two numbers, you can draw lines connecting them to see the angle between the hour hand and minute hand if they were to point at those numbers, or simply note their positions relative to each other on the clock face.

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