Number 6: Differences between Numbers in Pigeon Holes

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In summary, the conversation is about a problem involving ordered pairs and pigeon holes. The problem involves finding two numbers that differ by 11 using the given set of ordered pairs. The speaker suggests splitting the pigeons not equal to 1 and 100 in half to get at least 108 pigeons, but the questioner points out that there may be something wrong with the problem itself.
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ehrenfest
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Homework Statement


http://math.stanford.edu/~vakil/putnam07/07putnam1.pdf
I am working on number 6.

Consider the the ordered pairs (1,12),(2,13),...,(89,100). There are 89 of them. These are the pigeon holes.

There are 55 numbers between 1 to 100 and each of them flies to one or two pigeon holes. So split all of the pigeons not equal to 1 and 100 in half to get at least 108 pigeons. Then we have 108 pigeons flying to 89 holes. So there must be two numbers that differ by 11.

What is wrong with my logic?


Homework Equations





The Attempt at a Solution

 
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  • #2
Maybe there is something wrong with the problem instead...
 
  • #3
anyone?

This problem is really bugging me!
 
  • #4
please--I am probably just making a stupid mistake and I want to fix it!
 

What is the difference between two numbers?

The difference between two numbers is the result of subtracting the smaller number from the larger number. This can be represented using the mathematical symbol "-", where a - b = c and c is the difference between a and b.

How do you find the difference between positive and negative numbers?

To find the difference between positive and negative numbers, you simply ignore the signs and subtract the two numbers as if they were both positive. The resulting difference will have the same sign as the larger number.

What is the absolute difference between two numbers?

The absolute difference between two numbers is the positive value of the difference between those two numbers. This means that the resulting value will always be a positive number, regardless of which number is larger.

What is the difference between a whole number and a decimal number?

The main difference between a whole number and a decimal number is that a whole number is a number without any decimal or fractional parts, while a decimal number contains a decimal point and digits after it. Whole numbers are typically used for counting and whole quantities, while decimal numbers are used for measurements and precise calculations.

How can I calculate the difference between two numbers using a calculator?

To calculate the difference between two numbers using a calculator, you can use the subtraction function. This is usually represented by the symbol "-", and you simply enter the two numbers and press the subtraction button to get the difference. Some calculators may also have a dedicated "difference" button for this calculation.

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