Advanced Jumpy Jackpot

Transcript

Advanced Jump JackpotThe game can be made more difficult when Grumpy places two treasures on two different numbers. Jumpy must choose a single jump size that allows him to land on both treasure numbers, starting his jumps from 0. For example, if treasures are placed on 14 and 36: If Jumpy chooses a jump size of 7, he will jump to 7→14→21→28→35→42.... In this case, he lands on 14 but does not land on 36, so he does not win the treasures. To find a winning jump size, Jumpy must choose a number that is a factor of both treasure locations. The factors of 14 are: 1, 2, 7, 14. The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, and 36. The jump sizes that will successfully land on both 14 and 36 are 1 and 2. These numbers are the common factors of the two treasure number Factors of 14 Factors of 36 [In detail] Finding common factors of 14 and 36 We find factors of 14 & 36 separately 1 × 14 = 14 2 × 7 = 14 7 × 2 = 14 We stop here as 7 & 2 have occurred earlier So factors of 14 are 1, 2, 7, 14 1 × 36 = 36 2 × 18 = 36 3 × 12 = 36 4 × 9 = 36 9 × 4 = 36 We stop here as 9 & 4 have occurred earlier So factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36 So, Common factors of 14 & 36 are 1, 2