<p>Each of 5 men played a game of chess with each of 5 women, and then each woman played a game of chess with each of the other women. How many games of chess were played?</p>
<p>Answer Choices: </p>
<p>(A) 20 </p>
<p>(B) 25 </p>
<p>(C) 35 </p>
<p>(D) 45 </p>
<p>(E) 50</p>
<p>Is the answer 35? That’s the only that makes sense.</p>
<p>5 x 5= 25 (Men vs. Women)
4+3+2+1= 10 (Women vs. Women games)</p>
<p>25+10= 35 total games (Answer C)</p>
<p>Ah, this one was actually one of the more difficult ones they decided to put up on the site for all to see. </p>
<p>Since each of the 5 men play a game of chess with each of the 5 women, each man plays 5 games. Continuing, there are 5 men, so 25 inter-gendered games are played. Then, each woman plays games with one another, so that comes out to another 10 as they can’t play the same person twice. </p>
<p>25 games (between men and women) and 10 games (women-women) = 35 games in all</p>
<p>Yeah I get the 25 part of men to women with 5x5.</p>
<p>But it’s just the part where 10 I do not get that made me get the wrong answer.</p>
<p>If each of the five men play a game with each of the five women, that’s five games per man for a total of 25 games. </p>
<p>If each of the women played a game with each of the four other women, you could count the games with the first woman having 4 games, the second 3 games (the fourth woman is included in the first count), the third 2 games, the fourth woman 1 game, and the fifth woman 0 games. That’s a total of 35 games. </p>
<p>Here’s another way of looking at it: the word is the woman, the number represents the other woman sheplays against. If there are parentheses, the game has been counted in a line above. If you count the numbers without parentheses, there is a total of 10 games played between the women.</p>
<p>First 2 3 4 5
Second (1) 3 4 5
Third (1) (2) 4 5
Fourth (1) (2) (3) 5
Fifth (1) (2) (3) (4)</p>
<p>That was long and kind of confusing, haha. Did that make any sense to you?</p>
<p>
</p>
<p>This was well explained.</p>
<p>take the group of men to consist of A, B, C, D and E and the women of Q, W, E, R, T</p>
<p>
</p>
<p>For A, the games were<a href=“A”>/u</a>---------(Q)
(A)---------(W)
(A)---------(E)
(A)---------(R)
(A)---------(T)</p>
<p>So A played 5 games. Similarly B, C, D and E must have also played 5 games each. That makes a total of 5*5=25 games.</p>
<p>
</p>
<p>(Q)---------(W)
(Q)---------(E)
(Q)---------(R)
(Q)---------(T)
^4 games</p>
<p>(W)---------(E)
(W)---------(R)
(W)---------(T)
^3games</p>
<p>(E)---------(R)
(E)---------(T)
^2 games </p>
<p>(R)---------(T)
^1 game</p>
<p>Add them up, 4+3+2+1=10</p>
<p>Now add 10 to the 25 from earlier and you get 35.</p>
<p>^Lol, most complete explanation yet.</p>
<p>Alright, I’m glad part of that was clear! </p>
<p>The other (simpler) way to think about the women is as a combination where n=5 and r=2, since order is unimportant and repetition is not allowed.</p>
<p>Simple/Quick way 5*5 = 25 + (1 + 2 + 3 + 4) = 35</p>
<p>Man #1 vs. Woman #1, #2, #3, #4, #5 (5 games total)
Man #2 vs. Woman #1, #2, #3, #4, #5 (5 games total)
Man #3 vs. Woman #1, #2, #3, #4, #5 (5 games total)
Man #4 vs. Woman #1, #2, #3, #4, #5 (5 games total)
Man #5 vs. Woman #1, #2, #3, #4, #5 (5 games total)</p>
<p>Men vs. Women Total = 5+5+5+5+5 = 25</p>
<p>Woman #1 vs. Woman #2, #3, #4, #5 (4 games total)
Woman #2 vs. Woman #3, #4, #5 (3 games total)
Woman #3 vs. Woman #4, #5 (2 games total)
Woman #4 vs. Woman #5 (1 game total)</p>
<p>Women vs. Women Total = 4 + 3 + 2 + 1 = 10</p>
<p>25 + 10 = 35 games total</p>