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# Mathematics - Other

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If lines are drawn on a map, a triangle can be formed by the cities of New York City, Washington, D.C., and Buffalo, New York. On the map, the distance between New York City and Washington, D.C. is 2.1 cm, New York to Buffalo is 2.5 cm, and from Buffalo to Washington D.C. it is approximately 2.85 cm. If the actual straight-line distance from Buffalo to Washington is 285 miles, how far is it between the other pairs of cities?

https://brainmass.com/math/functional-analysis/mathematics-other-224494

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## Discrete Math: Integers

A US Social Security number is a nine-digit number. The first digit (or digits) may be zero.
a) How many US Social Security numbers are available?
b) How many US Social Security numbers are odd?
c) How many US social security numbers read the same backward and forward (eg 350767053)?

a) How many 4-digit numbers do not contain number 5 among its digits?
b) How many 4-digit numbers contain at least one number 5 among its digits?
c) How many 4-digit numbers contain exactly one number 5 among its digits?

Prove that if a is an odd integer, then a^2 + 7 is divisible by 4.

Read very carefully each of these sentences. Then, complete them:
a) The only integer which is divisible by every other integer is...
b) The integers that divide all prime numbers are ... and ...
c) If p is a prime number, it has ... positive divisors, and ... integer divisors.
d) (See the attachment for the equation)
e) Which one is larger, 2^1000 or 500! ? The answer is ...
f) The set {{2,6},{3,6}} has exactly ... elements. Does it coincide with {2,3,6}?

Prove that 99^4 divides 100!-99!

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