Hard math/logic questions!!!?

Question

Please help me on these! ive been stuck on them all week! Please show me how they are done too so i can learn too.

1. A child was born in Boston, Massachuesettes, to parents who were also born in boston. The child is not automatically a US citizen, how is this possible?


2.What is the 99th letter in the pattern below?

ABBCCCDDDDEEEEE...


3. In how many ways can you make change for $20 using only quarters and dimes, with atleast one of each coin used?


4. The number 1961 has rational symmetry, because the number looks the same when turned 180 degrees, find the next greatest number that also has this feature.


5. Show how half of 13 can possible be eight.

6.How mcuh money would you make in 8 days if you made 8 dollars everytime the hands of a clock formed a 90 degree angle?

Please try and answer as many as possible and THANK YOU SO MUCH!!!

Answer 1

1. The parents could have been foreign diplomats and the baby could have been born in a foreign embassy in Boston, MA. This is considered foreign soil. Or it could be before Boston was a state.

2. 1 + 2 + 3 + 4 + 5 + ... + n = n(n+1)/2
So what value makes n(n+1)/2 >= 99?

n(n+1) >= 198
14(15) = 210

With 14 letters, that will be a total of 105 in the pattern, so the 99th letter in the pattern will fall on an N.

3. Start with all quarters and replace them with dimes in a methodical manner.
$20 = 80 quarters
$20 = 78 quarters, 5 dimes
$20 = 76 quarters, 10 dimes
$20 = 74 quarters, 15 dimes
...
$20 = 4 quarters, 190 dimes
$20 = 2 quarters, 195 dimes
$20 = 0 quarters, 200 dimes

That is 41 ways.

4. After 1961 we get to 2nnn, 3nnn, 4nnn, etc. The next time there will be rotational symmetry will be in the year 6009.

5. Take roman numeral XIII and divide it in half horizontally. The result is VIII

6. We assume that the hour hand moves continuously just as the minute hand moves. So at 12:15, the hands aren't exactly at 90 degrees. (Hour hand is a few degrees off of 12). Instead, it will be slightly later, but it will be 90 degrees at some point.

It seems like it should be 12 times every hour, but we actually lose a complete revolution. The time between alignment will actually be 11 times every 12 hours. However there is also the second case when they are 270 degrees apart (which is technically also 90 degrees the opposite way). That makes 22 times every 12 hours, or 44 times a day.

44 times/day * 8 days * $8 = $2,816

Answer 2

I'll see what I can do to help though I may not be able to solve them all.
1. I'm not sure because if the parents were born in Boston MA too, then the law of Jus Sanguinas takes place, and if born in Boston MA, the law of Jus Solis applies to 55

2. Add 1+2+3+4+5+6+7+8+9+10+11+12+13+14 =105. So that means the 14th letter in the alphabet is letter 99, so "N" I believe

3. Not sure about number 3, have an idea but too much work lol

4. You just have to find the next leading numbers that look the same when turned upside down. 8 is the only other digit that looks the sme upside down so the answer is 6009. Puzzling is right lol as he pointed out to me.

5.Dunno

6. Technically it would be ver little because the only time that would really happen is at 3:00 and 9:00 since the hour hand moves subtlely as the minute hand moves so if you multiply 8 by 2 you get 16 abd 16 times 8 = 128

Oh and that Puzzling guy is smart I. I just saw his post but the answer where he put 1881 is wrong because it asks for the next largest number.

Answer 3

many have already answered. so i'll just try the ones where my answers aren't the same as before.

q3
most quarters + least dimes
= 78 (1/4) + 5 (1/10)
= 20

most dimes + least quarters
= 195 (1/10) + 2 (1/4)
= 20

changing 2 quarters into 5 dimes everytime, there's 38 times changing to get the most be the least (and reversing) so 39 combination in all.

q4
if you count the "calculator" / digital numbering, then answer is 2002. if it's with this font, then 6009 should do.

q6
each day the 2 hands overlap 22 times. so 90 degrees before AND after, that's double the number, is 44. so answer
= 44*8*8
= $2816

Answer 4

Dj, yet then how will each and each guy or woman get the piece that they want? i think of it must be something like this: Alice cuts a million/3 (as truthful as she can) Bob receives to compliment no count if to take that 0.33 or shrink the the rest 2/3 If Bob takes the a million/3 (he theory it became larger than a million/2 of the the rest cake) then Alice receives to shrink, and Cheryl receives to %.. Alice receives the final piece. Then that is truthful. If Bob cuts, then Alice receives the piece she shrink, and Cheryl techniques out of the two products Bob shrink. Bob receives the final piece. that is truthful because of fact if all of us attempts to get greater beneficial than their share, they're going to surely finally end up with the smallest piece!

Answer 5

1. It happened before the U.S existed (Massachusetts was just a colony)

Answer 6

These are easy just try I am sure you can do it.
P.S. I am not giving you the answers