<p>In a certain game, each token has one of three possible values: 1 point , 5 points or 10 points. HOw many different combinations of these token values are worth a total of 17 points ?</p>
<p>the answer is 6 ??? but how ??</p>
<p>Yeah, I also did the same.(actually, I happened to stumble upon this same problem just a few minutes ago)!</p>
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<p>“How many positive integers less than 100 are multiples of 5 and are equal to 3 times an even integer?”</p>
<p>For that one, you have to realize that we are looking for numbers that must be even numbers (as an odd number times and even number always results in an even number) and are multiples of 5. Thus, we are strictly looking at the 10s (ie 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100) since they are even numbers, and are divisible by 5. Because the numbers must be 3 times and even integer, we can assume that the numbers in question are divisible by 3 as well. The only numbers in this range that works is 30, 60, and 90. Thus 3.</p>
<p>You can extend this to 1000. What you did is also correct mathematically. We were looking for numbers that are multiples of 5 (which is a fifth of those numbers) AND numbers that are mutliples of 6 (which is a sixth of those numbers), which means that a thirtieth of the numbers of the range in question fullfills these expectations. You would round down as we know both end points do not fullfill the expectations in question.</p>
<p>In a certain game, each token has one of three possible values: 1 point , 5 points or 10 points. HOw many different combinations of these token values are worth a total of 17 points ?</p>
<p>the answer is 6 ??? but how ?</p>
<p>@ahmed
Case 1: 2<em>1+5+10
Case 2: 2</em>1+3<em>5
Case 3: 7</em>1+10
Case 4: 7<em>1+2</em>5
Case 5: 12<em>1+5
Case 6: 17</em>1</p>