It’s always exciting when movie characters get into a big swordfight — and even more so when real people do it as a sport, called fencing. In competitive fencing, the contestants aren’t just clashing their swords together to make alarming noises. To be clear, they’re both trying to stab each other — which is fine, because they’re both wearing thick protective clothing and masks. They score a point for each “touch” to their opponent on allowed body areas, hence the exclamation “Touché!” Contestants can fence with a foil, which is a very thin bendy sword; an epee, which is much heavier; or a saber, which can score with either the tip or the side of the blade. By learning the right tricky moves, you can parry (block your attacker’s weapon), counterattack, or fake out your opponent by starting to attack in one direction and then lunging in another. Even with no one’s head getting cut off, it’s plenty exciting for the people watching.
Wee ones: In fencing the styles of weapon are the foil, épée, or saber. How many choices of weapon is that?
Little kids: If you attack your opponent to the high line (above the bellguard, the cup over the handle of the weapon) then the low line (below the bellguard), then to the inside, then to the outside, then repeat high-low-in-out over and over, what’s your 8th attack? Bonus: What’s your 11th attack?
Big kids: When fencing with the foil, only touches to the body with the tip of the foil count. If during a bout you make 31 touches but 13 of them are to the arms and legs and don’t count, how many possible touches does that leave? Bonus: If 1/3 of those were with the side of the blade, which also don’t count, how many touches count?
The sky’s the limit: In a bout, the first player to score 15 touches wins; if neither reaches 15 within 3 minutes, whoever has more points is the winner. What are all the possible non-tie scores those 2 contestants can have with either contestant winning?
Wee ones: 3 weapons.
Little kids: To the outside. Bonus: To the inside.
Big kids: 18 possible touches. Bonus: 12 touches, since 6 were ruled out.
The sky’s the limit: 240 outcomes. If we start with A winning over B, A can have anywhere from 1 to 15 touches, and for each of those B can have any score up to 1 less than A’s score. So B can have just 1 score (0) if A wins with 1; 2 possible scores (0 or 1) if A wins with 2; 3 possible scores (0, 1, or 2) if A wins with 3, and so on up to A winning with 15 and B having any of 15 scores. So it’s a triangle number adding all numbers up to 15, which comes to (15×16)/2 = 120. Then we can have all those same combos with B winning, giving us 240 possible outcomes.
And a big thank-you to Lane R. for inspiring this BMP topic!