To: HIQ From: D5B (Jon Ripley) Subject: Question Answers Pt.2 Here are the answers to the last three questions... These questions dealt with adding together the digits of a number to make another number, so for the number 1234 you would add 1+2+3+4 to make 10, and because you still have more than 1 digit you would add 1+0 to make 1, the final answer. 8. 184 = 1+8+4 = 13 = 1+3 = 4! 9. 98832365 = 9+8+8+3+2+3+6+5 = 44 = 4+4 = 8 10. 4444 4444 ? 4444 ? This one was a bit more difficult! You could either take it as a trick question leaving. 4+4+4+4+4+4+4+4 = 32 = 3+2 = 5 Or you could take it as a literal number and add all the digits in the number 4444 to the power of 4444 (ie 4444 multiplied by itself 4444 times!) I won't give the solution here as it is over 16,500 digits long, I can however, tell you that if you add all those digits together you get 7. In a future issue I may tell you how to calculate such large numbers. More puzzles coming soon! HIQ is moving across to BBC User Group if you have any puzzles/questions that you would like to see in this section in future issues, you are welcome to send them in to 8BS, or me at BUG. ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, To: HIQ From: D5B (Jon Ripley) Subject: Question Answers Pt.1 In a previous issue I posed a few questions for you to think about. Here are the answers! The next number in the sequence... 1. 3 4 5 8 1 7 7 10 3 ... The next number is 6. 2. 5 2 3 3 9 8 6 1 10 ... The next number is 3. Congratulations to those of you who managed to work these out. If you are still in the dark, they are the first 10 numbers produced by the typing the following after switching your BBC on. FOR X=1 TO 10:PRINT RND(10):NEXT Question 1 is the numbers given using BASIC 4 on the Master. Basic 2 on Electrons, BBCs and some B+s gives the numbers in question 2. 3. 1 3 6 10 15 ... This is a simple numerical series where each number in the list is the position of the number in the list added to the previous number, thus... 0+1=1, 1+2=3, 3+3=6, 6+4=10, 10+5=15 so the next number is 21 or 15+6. Next you were asked to find the next 2 numbers in a series. 4. 9 1 8 2 7 3 ... The next two numbers are 6 and 4, each pair of two numbers adds up to 10. Another way of looking at it is as two superimposed series, one going 9 8 7 6 and the other going 1 2 3 4 etc. 5. 3 1 4 1 5 ... There are two answers to this one, it could be 1 then 6 if you see it as a list of consecutive numbers with a 1 separating them, if so the series would continue with 1 7 1 8 1 9 1 etc. The second way of seeing this is as the digits of PI, which are 3.1415926 etc. So the next two digits in the sequence would be 9 then 2. 6. 12 23 34 45 54 43 ... If you think of this one without thinking of maths you will notice a pattern. With 32 and 21 being the next two numbers. 7. What is 9.11612581436 ? 'A number!' is the first obvious answer that springs to mind, although you will technically be correct you would have answered incorrectly. This is in-fact another PI related question. If you take a closer look at the number you might notice that it consists of a sequence of square numbers. (A square number is a number made by multiplying a number by itself, so 16 is 4 squared because 4*4=16.) Splitting this number into separate squares you will get... 9 1 16 1 25 81 4 36 Taking the root of the squares you get the numbers: 3 1 4 1 5 9 2 6 which are of course the digits of PI. The answers to the last three questions are in the next message!