### Thursday, February 2, 2012

#### Given sum and product, find the two integers.

I gave my grandson the following puzzle: The sum of two integers is 20. Their product is 91. What are the two integers. He figured it out by: 1 * 19 = 19. Too small. 3 * 17 = 51. Too small. 5 * 15 = 75. Too small. 7 * 13 = 91. Just right. I showed him the following way to solve it, that would work...

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### Monday, January 23, 2012

#### Enhancing Fermat Factoring

Enhancing Fermat Factoring How would we most quickly determine two positive integers which, when multiplied together, make 2047? One way would be to make use of Fermat factoring. If t^2 - s^2 = 2047, then (t-s) * (t+s) = 2047. We can search for values of t and s that solve this equation. Once we...

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### Friday, January 6, 2012

#### Calendar Calculation

Pocket Calendar Memorize the number pattern for leap year, 034 025 036 146. Now overlay this pattern with January February March April May June July August September October November December. For non-leap years, memorize the pattern 033 614 625 035. For each year, determine which day of the week is...

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### Wednesday, October 26, 2011

#### Mathematical induction

The basic idea of mathematical induction is this: Suppose you wish to prove that a statement is true of all positive integers. You can easily prove that it is true for the integer k=1. You can also prove that in general, if it is true of the integer k, then it is also true of the integer (k+1). This...

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### Thursday, October 6, 2011

#### Excerpt_0002

The Book of Numbers by John H. Conway and Richard K. Guy Chapter 1 The Romance of Numbers Hickory, Dickory, Dock --- Eeny,Meeny, Miny, Mo There are several systems of words for numbers that survived for special purposes in out-of-the-way places. The particular sequence of words varies both with the...

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### Tuesday, October 4, 2011

#### Excerp 0001

The Book of Numbers by John H. Conway and Richard K. Guy Chapter 1 The Romance of Numbers Number Words Throughout history, NUMBER and NUMBERS have had a tremendous influence on our culture and on our language. Thousands of words are obviously associated with numbers. For example: A monologue is a...

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### Monday, September 26, 2011

#### Number string puzzle solution

Number string puzzle solution 8 digit number: first digit is 9 minus 8th digit. second digit is 9 minus 7th digit. third digit is 9 minus 6th digit. fourth digit is 9 minus fifth digit. All 8 digits are different. None of the digits are zero. None of the digits are 9. The second and first digit...

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### Friday, September 23, 2011

#### Number string puzzle

8 digit number: first digit is 9 minus 8th digit. second digit is 9 minus 7th digit. third digit is 9 minus 6th digit. fourth digit is 9 minus fifth digit. All 8 digits are different. None of the digits are zero. None of the digits are 9. The second and first digit differ by 2. The second and third...

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### Tuesday, September 20, 2011

#### Typical "find their ages" word puzzle

In another ten years Bob will be twice the age of Adrian. Ten years ago, Bob was three times the age of Adrian. How old are Bob and Adrian?

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### Sunday, September 18, 2011

#### Elementary Number theory theorem: Adding to prime

Give examples of and prove the following theorem about integers. If A, B, and k are positive integers such that: A > B > 1; A and B are relatively prime; For every positive prime, p, such that p < k, either p divides A or p divides B: Then it is true that if A+B < k^2 (meaning k squared), then A+B...

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