Which positive whole number is the lowest that cannot be scored with two darts?

TabbyTom

Assuming that both darts have to score, I make it 103. Dec 14 03, 1:10 PM

gmackematix

I think a yay to TT here for 103. Even if one dart misses you can score anything from 1 to 20. If one dart hits 20, with the other the totals 21 to 40 are easily achieved. If one dart hits 60, then doubles give every even number from 62 to 100. If one dart hits 57 (treble 19), then doubles give every odd number from 59 to 97. If one dart hits 60 then trebles give every number that divides by 3 from 63 to 120. If one dart hits 50 then trebles give every number with remainder 2 when divided by 3 from 53 to 110. The smallest number not achievable by these combinations is 103. That's a lot quicker to work through in the head than it is to type! Dec 14 03, 8:48 PM

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Find two whole, positive numbers that have the same answer when multiplied together as when one is divided by the other? Which of the two rival World Darts Championships has the bigger prize for the winner? Find three whole, positive numbers that have the same answer when multiplied together as when added together? Take any positive whole number not greater than 50. If the number is even, divide it by two. If the number is odd, multiply it by 3, and add 1 to the result. Apply the same method to the resulting number, and continue in this way forming a chain of numbers untill you finally arrive at the number 1.Shown below is a chain of numbers that results from this method if you begin with 15: 15 - 46 - 23 - 70 - 35 - 106 - 53 - 160 - 80 - 40 - 20 - 10 - 5 - 16 - 8 - 4 - 2 - 1. As you can see, the number 15 requires 17 steps to end up at 1. Of the numbers not greater then 50, which takes the longest to reach the number 1?

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