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One thing that's bothered me about the archive solution is that it asks about the general case of any number n coins, but then it only gives a solution for certain 'nice' n's; particularly:
n = (3^w
A friend's house has a burglar alarm with a ten-digit keypad which takes a four-digit number to disarm it. Unfortunately the four digits in the number are the only keys ever used, and these four digit
... each square using two opposite quadrants of the circle. This raises some questions:
What is the fewest number of pieces that you would need in order to use them to create the silhouette of a square...
I have been going through Oystein Ore's book 'Number Theeory and Its History'. Great read and he does a fantastic job upto and including linear Diophantine problems and the Pythagorean numbers, but th
You are paging through an almanac with entries involving the areas and populations of thousands of countries, states, provinces, counties. towns, villages, townships, islands, etc.
About what percen
...ntical to row B ?? (of course initial ordering were different and identical means row A will contain same number of heads and tails as row B at similar positions. ie if the ordering of B is HTHTHHTHHH...
...gers (e.g., 1 through N) are written on a piece of paper. The two players take turns selecting one of the numbers on the piece of paper and crossing it off. After a number has been selected, it can't ...
... them, post questions to get an answer, I would be honest in saying that in my day to day job I don't use numbers and my use of math stopped quite a few years ago, and so any number puzzles put me off...
Can someone find the next 3 numbers in the following series ?
34631, 22203, 14745, 10095, 8649, 6933, 5533, 4580
Bonus question : What is so special about this series ?
Happy Hunting !
...2 81=9^2 9=8+1 512=8^3 8=5+1+2 2401=7^4 7=2+4+0+1 ...
The question: Is there for every exponent B a basenumber A, with the (sum of the numbers of A^B)=A ??
Is there an example with the exponents 5...
...uper Bowl wins the pot. Some people submit multiple entries to increase their chances of winning. Are the number of possibilities simply a matter of 8*7*6*5*4*3*2*1, or do the multiple rounds and dual...
These are the CORRECTED results to Numbers Contest NUM4.
Hi. Gerrit de Blaauw pointed out that there was a mistake in the scoring of the last contest. A single '6 ' in question F was read by the sco
...ings. The rings were colored yellow, blue, and red. The yellow ring was the largest, and scored the least number of points. The red 'bulls-eye' ring was the smallest, and scored the most number of poi...
...00+1), on the other hand, consists of 2000 9's, and therefore has a different sum - 18000.
The smallest number is thus 10^1000+1....
...obe's error, and despite two more steps of conversion and rounding, the 'World' ended up with the correct number.
For ANY integer number of knots, what is the probability that the 'World' ends up wi...
...an recall of the circumstances. Second, if anyone manages to do a game in one round, let me know the game number - I'm quite interested to know how many of them are solvable. (FYI, as I said before, I...
What is the next number in the following sequence?
12,345,678 12,345,687 12,345,768
... Odds of winning $250 are 1 in 3198.'
Earlier in the letter was the statement that I was one of a small number of people randomly selected to complete the survey. Hmmm, I wonder what the total numbe...
...was playing (I can't remember what the game was). From a given integer range 1...n, he would have to pick numbers which he got to add to his total, and his opponent would get the remaining factors of ...
...a successor function that takes one permutation and produces the next.
(The equivalent of adding 1 to a number, except that the equivalent of 'carry' is a bit more messy. :-)...
...ading zero, if necessary) the positive difference between the squares of the two parts gives the original number.
Thus, 216513 is excellent because it is equal to 513^2 - 216^2.
How many excellent...
...atic, and thus equally highly intelligent. 2) Everyone who enters knows #1 (and successive iterations) 3) Number of entries tends to be around 35-40 entrants.
Question: provide a positive integer.
...
...and all can keep the device. So now everybody wants to access the settings menu and change the ISP dialup number... That's the background on this challenge, so nothing illegal for those that were wond...
Don't need spoiler space for this one...
We were talking about hotels with infinite numbers of rooms recently...
how about
...ove geometrically: Plot time on the x-axis and distance from the bridge on the y-axis, say, with positive numbers standing for movement in the direction of the river flow. Draw a line from the origin ...
...e city and 75% of the time on the highway. Which of the four cars listed below will give him the greatest number of miles per gallon of gasoline?
average miles average miles per gallon per gallon in...
You have a rod one unit in length. You generate four random numbers between 0 and 1.
You cut the rod at the points indicated by the lowest and the highest of these four numbers, measuring each point
...his is from http://www.iqtest.dk/main.htm
can somebody help me with those, i can't get them:
5. Which number should replace the quiestion mark?
8 4 3 8 2 7 6 9 6 1 5 1 ? 5 4
a 4 b 3 c 6 d 8 e ...
... passed since the last broadcasting of each listed program type. Performing certain operations with these numbers, and possibly introducing some other factors too, would derive the sought index for th...
...nitessimally, and the basic argument you gave would have been the same if we were just talking about pure numbers rather than money (I write down two numbers n and 2n and put them in an envelope, and ...
... a week. I couldn't solve it. It looks like very easy problem. The is the just like following. 1.Find the number of circular arrangements of r ones and n-r zeros with no ajacent ones.
2.Find the num...
...he pirates are all highly intelligent The pirates are all greedy but cautious - they want to maximise the number of coins they get, but will not risk losing any coins, and will avoid death at all cost...
... by floor(n/2) or ceiling(n/2) 5) Return to line(2) if n is odd 6) If n >= 500 then dead-end. 7) Subtract number of positive divisors of n 8) Add 1 or 2 9) Add squareroot of largest perfect square = 2...
Here is a problem on expressions for successive integers by J.A.H. Hunter.
It's the Numbers Game today, with 4433. Using all four each time, but only the two 4s and two 3s, and no other figures at a
1. Take N = K*(K+1)/2 cards where K is any natural number. 2. Divide the N cards to a number of packs (equally or not). 3. Take one card from every pack and form a new pack from these cards. 4. Repeat
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