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Square Numbers

by Anonymous
(United Kingdom)










































tom has 4 number cards; 4 6 9 and 1. what is the difference in the 2 square numbers he can make?

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Nov 20, 2011
Square Numbers
by: Staff

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Part II


“B”

If you use all four digits (4, 6, 9, and 1) to create every possible 3 digit number

Sampling without replacement
Ordered sample

n = 4 (4 numbers to choose from)
r = 3 (choose 3 numbers at a time)

P(n,r) = n!/[(n-r)!]

= 4!/[(4-3)!]

= 4*3*2*1/[(1)!]

= 4*3*2*1/1

= 24/1

= 24 combinations possible if you select 3 numbers at a time

These are:

{4,6,9} {4,6,1} {4,9,6} {4,9,1} {4,1,6} {4,1,9} {6,4,9} {6,4,1} {6,9,4} {6,9,1} {6,1,4} {6,1,9} {9,4,6} {9,4,1} {9,6,4} {9,6,1} {9,1,4} {9,1,6} {1,4,6} {1,4,9} {1,6,4} {1,6,9} {1,9,4} {1,9,6}

The square root of each of these numbers is:

√146 = 12.08305
√149 = 12.20656
√164 = 12.80625
√169 = 13
√194 = 13.92839
√196 = 14
√416 = 20.39608
√419 = 20.46949
√461 = 21.47091
√469 = 21.65641
√491 = 22.15852
√496 = 22.27106
√614 = 24.77902
√619 = 24.87971
√641 = 25.31798
√649 = 25.47548
√691 = 26.28688
√694 = 26.34388
√914 = 30.23243
√916 = 30.26549
√941 = 30.67572
√946 = 30.75711
√961 = 31
√964 = 31.04835




Thanks for writing.

Staff
www.solving-math-problems.com


Nov 20, 2011
Square Numbers
by: Staff

Part I

Question:

by Anonymous
(United Kingdom)

tom has 4 number cards; 4 6 9 and 1. what is the difference in the 2 square numbers he can make?


Answer:

A square number is a perfect square. A perfect square is an integer which is the square of another integer (eg: 25 is a square number because 25 = 5²).



I. FOUR DIGIT Numbers. If you use all four digits (4, 6, 9, and 1) to create every possible 4 digit number (see calculations under “A” below):

1) there are exactly 24 POSSIBILITIES.

2) NONE of the 4 digit numbers created using all four digits IS A SQUARE NUMBER.



II. THREE DIGIT Numbers. If you use all four digits (4, 6, 9, and 1) to create every possible 3 digit number (see calculations under “B” below):

1) there are exactly 24 POSSIBILITIES.

2) THREE of the 3 digit numbers created from the four digits (4, 6, 9, and1) ARE SQUARE NUMBERS: 169 = 13²; 196 = 14²; 961 = 31².



The final answer:

There are at least three answers to your question:

1) 961 - 196 = 765
2) 961 - 169 = 792
3) 196 - 169 = 27





“A”

If you use all four digits (4, 6, 9, and 1) to create every possible 4 digit number:

Sampling without replacement
Ordered sample

n = 4 (4 numbers to choose from)
r = 4 (choose 4 numbers at a time)

P(n,r) = n!/[(n-r)!]

= 4!/[(4-4)!]

= 4*3*2*1/[(0)!]

= 4*3*2*1/1

= 24/1

= 24 combinations possible if you use all 4 numbers


These are:

{4,6,9,1} {4,6,1,9} {4,9,6,1} {4,9,1,6} {4,1,6,9} {4,1,9,6} {6,4,9,1} {6,4,1,9} {6,9,4,1} {6,9,1,4} {6,1,4,9} {6,1,9,4} {9,4,6,1} {9,4,1,6} {9,6,4,1} {9,6,1,4} {9,1,4,6} {9,1,6,4} {1,4,6,9} {1,4,9,6} {1,6,4,9} {1,6,9,4} {1,9,4,6} {1,9,6,4}

The square root of each of these numbers is:




√1469 = 38.32754
√1496 = 38.67816
√1649 = 40.60788
√1694 = 41.15823
√1946 = 44.11349
√1964 = 44.31704
√4169 = 64.56779
√4196 = 64.77654
√4619 = 67.96323
√4691 = 68.49088
√4916 = 70.11419
√4961 = 70.43437
√6149 = 78.41556
√6194 = 78.70197
√6419 = 80.11866
√6491 = 80.56674
√6914 = 83.15047
√6941 = 83.31266
√9146 = 95.63472
√9164 = 95.72878
√9416 = 97.03608
√9461 = 97.26767
√9614 = 98.05101
√9641 = 98.18859

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