Question 153391: The number 1 is both a smute and thripe. If the integer s is a smute, then the next smute is s+5. If the integer t is a thripe, then the next tripe is 2t+1. What is the SMALLEST whole number GREATER than 1, that is both a smute and a thripe?
Answer by mducky2(62)   (Show Source):
You can put this solution on YOUR website! The easiest way to solve this problem is just to make a list of the numbers, starting from 1. When we do this for both smutes and thripes, the first integer that is on both lists (other than 1), that should be the answer.
Smute sequence:
1: 1
2: 1 + 5
3: (1+5) + 5 = 11
4: (1+10) + 5 = 16
5: (1+15) + 5 = 21
6: (1+21) + 5 = 26
7: (1+26) + 5 = 31
Thripe sequence:
1: 1
2: 2(1) + 1 = 3
3: 2(3) + 1 = 7
4: 2(7) + 1 = 15
5: 2(15) + 1 = 31
We don't even have to solve the rest. We can see that 31 appears on both the lists, and therefore is the smallest whole number that is both a smute and a thripe.
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