    Hard Puzzles  Puzzle 1 What is the next number in the sequence: 32 35 40 44 52 112 ==?== [Puzzle Code = ZGLU] Copyright © Kevin Stone    Direct Link: www.brainbashers.com?ZGLU Hint: A tricky question related to number bases. Answer: 200. Each number in the sequence is a representation of the number 32 in different bases, starting with base 10. Base 10: 32  = 3 x 10^1 + 2 x 10^0          = 3 x 10 + 2         = 32 Base 9 : 35  = 3 x 9^1  + 5 x 9^0           = 3 x 9 + 5          = 32 Base 8 : 40  = 4 x 8^1  + 0 x 8^0           = 4 x 8 + 0          = 32 Base 7 : 44  = 4 x 7^1  + 4 x 7^0           = 4 x 7 + 4          = 32 Base 6 : 52  = 5 x 6^1  + 2 x 6^0           = 5 x 6 + 2          = 32 Base 5 : 112 = 1 x 5^2  + 1 x 5^1 + 2 x 5^0 = 1 x 25 + 1 x 5 + 2 = 32 Base 4 : 200 = 2 x 4^2  + 0 x 4^1 + 0 x 4^0 = 2 x 16 + 0 + 0     = 32 Puzzle 2 Below you will find well-known eight letter words, with only their endings remaining. Can you determine the words? .....RUE .....JAR .....DIL .....ANY .....POX .....GTH .....ELF .....OIA .....IGE .....HOG .....TOO .....DIX .....FIN .....UPT [Puzzle Code = ZINF] Copyright © Kevin Stone    Direct Link: www.brainbashers.com?ZINF Hint: These are the first letters of the words: C, N, D, M, S, S, Y, P, P, H, C, A, P, B. Answer: .....RUE >> CONSTRUE .....JAR >> NIGHTJAR .....DIL >> DAFFODIL .....ANY >> MAHOGANY or EPIPHANY .....POX >> SMALLPOX .....GTH >> STRENGTH .....ELF >> YOURSELF .....OIA >> PARANOIA .....IGE >> PRESTIGE .....HOG >> HEDGEHOG .....TOO >> COCKATOO .....DIX >> APPENDIX .....FIN >> PARAFFIN .....UPT >> BANKRUPT Puzzle 3 Using the new BrainBashers programming language, BrainBasic, the following words have their equivalents next to them, what should FOX be? CLICK = 100501100K MILK  = 1000150K LOG   = 50OG LIFE  = 501FE ALIVE = A5015E FOX   = ==?== [Puzzle Code = ZWTB] Copyright © Kevin Stone    Direct Link: www.brainbashers.com?ZWTB Hint: Think of Roman numerals. Answer: FO10. Where Roman numerals exist they are replaced by their modern equivalents. CLICK = 100 50 1 100 K I = 1 V = 5 X = 10 L = 50 C = 100 D = 500 M = 1000 Puzzle 4 The Miller next took the company aside and showed them nine sacks of flour that were standing as depicted in the sketch. "Now, hearken, all and some," said he, "while that I do set ye the riddle of the nine sacks of flour. And mark ye, my lords and masters, that there be single sacks on the outside, pairs next unto them, and three together in the middle thereof. By Saint Benedict, it doth so happen that if we do but multiply the pair, 28, by the single one, 7, the answer is 196, which is of a truth the number shown by the sacks in the middle. Yet it be not true that the other pair, 34, when so multiplied by its neighbour, 5, will also make 196. Wherefore I do beg you, gentle sirs, so to place anew the nine sacks with as little trouble as possible that each pair when thus multiplied by its single neighbour shall make the number in the middle." As the Miller has stipulated in effect that as few bags as possible shall be moved, there is only one answer to this puzzle, which everybody should be able to solve. [Puzzle Code = ZYIT] The Miller's Puzzle. The Canterbury Puzzles And Other Curious Problems by Henry Ernest Dudeney (1907).    Direct Link: www.brainbashers.com?ZYIT Hint: The two left numbers multiplied, or the right two numbers, should create the central number. Answer: The way to arrange the sacks of flour is as follows: 2, 78, 156, 39, 4. Here each pair when multiplied by its single neighbour makes the number in the middle, and only five of the sacks need be moved. There are just three other ways in which they might have been arranged (4, 39, 156, 78, 2; or 3, 58, 174, 29, 6; or 6, 29, 174, 58, 3), but they all require the moving of seven sacks.      