superprismatic

I also tested more: Y <= 1,000,000 and found no more. The highest power of 5 I found with no 0s in the base ten representation was 558=34694469519536141888238489627838134765625 and the highest such power of 2 was 286=77371252455336267181195264 which means that their product is 268435456 followed by 58 zeros!

....what are the two numbers that I am missing that when multiplied together gives 10^x where x is

The telegram: 23224 17726 15411 27251 01812 13135 22166 14192 18209 [/code]was sent by a mysterious personage believed to be a secret agent codenamed Alex. Some time later the telegram: "My client cannot meet stated terms, considers twelve percent excessive. Also skeptical of broker's ability to pay current rates on speculative stocks, prefers advance payment without interest." was sent to the same addressee. The telegraph clerk became suspicious and put two and two together, thus averting a disaster. How?

There is no typo but Walter Penney has been known to introduce garbles into his problems to make them more realistic. He expects solvers to overcome such things. Just wait for what he has in store for everyone for Labor Day Weekend! Tomorrow's problem will test solvers's powers of perception much more than his previous problems have.

The first letter of a message is advanced a certain number of places in the normal alphabetical sequence, the second letter is advanced either the same amount or one more. (A follows Z.) Each letter is advanced either the same amount as the previous letter or one more, the flip of a fair coin determining which. The message (spaces are used only for ease of reading) emerges as LCZLP YVART SDUII ZKZAZ AGCIY AZKBQ QRGZT HBTCF CPIPE XYKTL LJHNH AQDVS BRT [/code]What does it say?

A sequence of numbers is generated by starting with an initial value n0 and computing subsequent values using the rule ni+1=ni+[sqrt(ni)]. Here [sqrt(ni)] represents the greatest integer in sqrt(ni). If n0 has no predecessor we shall call it a seed. For example, 11 is a seed since it cannot be produced by any number using the rule above. What is the seed corresponding to 1,000,000 (i.e., the unique value which generates the sequence containing 1,000,000 and which has no predecessor)?

Multiple sends are my service provider's fault. Sorry.

Multiple sends are my service provider's fault. Sorry.

Was the dropping of the word "of" in the question intentional, or was it a typo?

Right as rain!

cuberoot(3298 + 627550 * sqrt(-5)) + cuberoot(3298 - 627550 * sqrt(-5)) represents a certain positive integer N. If the digits of N are converted to letters (A=1, B=2, etc.), They spell a certain word. What is it?

In the game of Mathematical Hangman one player makes up an arithmetic problem which the other player tries to solve by asking whether certain digits occur in the various rows and columns. If the digit does not appear in the announced row or column, a part of the body is placed on the gallows. In a particular game one player made up a multiplication problem which fit into a 6x6 square; i.e., at least one digit touched each side of the square. Inspired guessing has elicited the information that in column F, 2 and 7 occur but 4 does not; in column E, 3 and 4 occur but 9 does not; in column D, 6 and 9 occur but 3 does not; in row J, 1 and 6 occur but not 8; in row K, 4 and 8 occur, but not 1; in row L, 1 and 2 occur, but not 7. The guessing participant is just one step away from being hanged. Can you save him by constructiong the problem with no more guesses? A B C D E F G x x x x x x H x x x ----------------- I x x x x x x J x x x x x x K x x x x x x ----------------- L x x x x x x [/code] SUPERPRISMATIC NOTE: Row H has 3 digits without a leading zero. At least one of the lines G, I, J, K, and L has no leading zeros.

Just think of the alphabet written around a circle. The distance between two letters is the shortest number of moves around the circle (either clockwise or counter-clockwise) to go from one letter to the other. This number is never greater than 13. I hope this makes things clearer to you. Oh, it is a rule of the proposed problem -- not just the example.

A certain five-letter word is to be determined as follows. A set of five-letter words is to be presented, the distances(less than or equal to 13) between letters of these words and the corresponding letters of the unknown word computed, and the product of these distances announced. For example, with JAUNT and the unknown word UNCLE, the value of this product would be 25168, since the respective distances are 11, 13, 8, 2, and 11. Consider the following test words and their product with an unknown word: EXIST--2772; JINGO--15360; MONEY--79200; OPERA--16380; RIDGE --46080; TODAY--41472. What is the unknown word?

To guarantee an acute triangle, I think that one must have 0 < b < a as well as c > sqrt(b*[a-b]). If (b,c) is too close to the x-axis the triangle will be obtuse.

Thanks. Your choices are precisely those that I got. I suppose that's the highest you can go.

Please post how many of each element you picked. The highest I found tied with Bushindo's solution, although it picked different elements than Bushindo did. I'd like to check yours.