How many 6-digit numbers are there where no three con- secutive digits are the same? (For values below 100000, assume we left-pad with explicit 0’s to make it 6 digits.) For example, we would count 123456, 648283, and 112233, but not 173334, 000123, or 111222.

A base-64 number system uses symbols A-Z, a-z, and 0-9 to represent the values 0-62, as well as "+" and "/" for the last two. What corresponds to the base-64 number Haze/ in decimal number? (Hint: H = 7, a = 26,e = 30,/= 63) O a. 108,447,072,047 O b. 23,892,203,551 O c. 31,599,764,303 O d. 101,160,045,438. e. 52,482,997,078

Convert the following numbers from base ten into the designated base. (a) 44ten (b) (c) 93ten (e) 151ten (d) 202ten (h) 72ten (i) = = (f) 403ten (g) 44ten = 144ten = (j) 200ten = 1252ten = five five two two tw sixteen six six sixteen five

c. Could you adapt Tylishia's method to other 183 49? If so, give at least two more examples subtraction problems, such as to the problem and show how to apply Tylishia's method in each 11. Tylishia says that she can calculate 324 - 197 by adding 3 to both numbers and calculating 327 – 200 instead. a. Draw a number line (which need not be perfectly to scale) to help you explain why Tylishia's method is valid. b. Explain in another way why Tylishia's method is valid. y -y ly, b- case. of

1. Consider a 4 digit number abcd and show that abcd−(a+b+c+d) is alwaysdivisible by 9. (Ex 1234 − 10 = 1224 = 9 · 136).   2. (A) How many different three-letter initials can a person have?(B) What if the initials are not repeated?(C) What if only consecutive initials are not repeated? ( please just answer part c on this one.. A and B are just so you know the entire question)

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This problem is about finding the missing digit of a code. I find it really hard to do please help.