# Crossword Puzzles from Beast Academy

I do love the Beast Academy books. My 3rd Graders are working on multiplication, and the Beast Academy books have these crossword puzzles. The kids love them:

(Why do the kids love them? Oh, I don’t know. If interest = “this is new” times “I can do this” then I guess this has enough going on that it feels new. And the puzzle is self-checking, which probably validates that “I can do it” feeling. That’s all I’ve got.)

Every puzzle can both be solved and studied. I’ve made it a habit to encourage my students to ask questions about the puzzles we solve, and I usually do this by sharing a question or two that I have.

My question was, can you make this puzzle using only multiplication?

And my kids’ questions were:

• Can you make one of these crosswords only using subtraction?
• Are the blanks really necessary?
• Could the puzzle be smaller? Larger? Could it be 5 x 4? 8 x 2?
• Could it be shaped like a path?

The next class, I gave students some blank crosswords and asked them to see if they could fill in the blanks in a way that worked.

Which was interesting. But the kids wanted more, so I sat down to make more crosswords in the original style. The original puzzles always include mostly multiplication, and then one addition and one subtraction equation, always on the right and bottom sides.

So I set out to make a few puzzles in this style. I started filling in the boxes, and got stuck. Then I tried again — still not working. I started to get that familiar good/bad feeling that happens with math. It’s the feeling of “oh this is harder than I thought” but also “there might be something here!”

Over lunch, I interrupted two of my colleagues and recruited them into the problem. (I was happy to return the favor after they’ve done the same to me so many times.) We filled out the crossword with variables.

Using these variables, the puzzle is only possible if $ac+bd =ab-cd$. My colleague pointed out that you might factor this a bit and then solve for d:

$d = \frac{a(b - c)}{(b + c)}$

A few things about that equation:

• It means that the whole puzzle is determined by just three of those variables.
• d is a whole number, so (b + c) needs to go into a(b – c).

This is not a ton to work on, but suppose that the sum of b and c is chosen to be a prime number. It clearly won’t go into (b – c). So that means a will have to be a multiple of b + c.

That seems to work!

This leaves me with a bunch of questions, though. Does this characterize all the possible crossword puzzles? I feel like this finds one specific way of getting a crossword that works here, but is it really the only way? Also, I haven’t really thought about whether I could use any multiple of b + c. I think I can, just because it’s worked whenever I’ve tried it so far, but it would be better to understand why.

There’s a math textbook that I like that makes the case that there is significant mathematics that has been developed by teachers, just for the sake of having nice examples to give to students. I always like when that sort of thing happens, a nice mathematical surprise that appears sometimes when you remember to look for it.

# Just the Jewish Parts of “ORIGINAL GANGSTAS: The Untold Story of Dr. Dre, Eazy-E, Ice Cube, Tupac Shakur, and the Birth of West Coast Rap”

Heller’s father owned a scrap metal business. He loved gambling on sports and hung out with the Jewish mob, eventually landing the family in wealthy Cleveland suburb Shaker Heights. As one of the town’s few Jews, Heller felt like an outsider, he wrote in Ruthless. (p. 68)

For Death Certificate Cube jettisoned the Bomb Squad and their pastiche approach in favor of more traditional slabs of chunky, midtempo funk, a production vision led by DJ Pooh and also featuring contributions from Cube, Sir Jink, Bobcat, and Rashad. The work was even more controversial than Amerikkka’s Most Wanted, absolutely unsparing in its critiques of Cube’s perceived foes, both personal and institutional. Most notorious os “No Vaseline,” directed at his former groupmates and one of the greatest diss tracks every recorded. The song’s good-time bounce only heightens in lyrics’ venom, accusing the N.W.A members of being gay and moving to white neighborhoods. They were essentially slaves to the “Jew” Herry Heller, the track insinuates, offering the suggestion, using the Nation’s preferred synonym for white men, the group should Get rid of the devil real simple / Put a bullet in his temple.

“[I]t proably hurt and affected me more than anything that’s ever been said or done to me,” Heller told an interviewer, adding that he faced anti-Semitism growing up. “I think he’s not anti-Semitic. I think he did it just because he thought it would sell records.”

“I’m pro-black. I’m not anti-anything but anti-poor,” Cube insisted when asked about the issue, adding that he worked with many Jewish people in the music industry.

Heller recruited as security director an Israeli named Mike Klein, whose job was to put the fear of God into their adversaries. Klein had a background in “Israeli security forces,” Heller wrote…Nobody seems to know the specifics of Klein’s background. Wrote Vibe: “Before he moved to Los Angeles, says somebody who knows him, the Israeli-born Klein ‘led a commando raid into southern Lebanon when they caught those guys who blew up the kibbutz kids on the school bus.’”

For further aid in their battle with Death Row, Klein and Heller enlisted the services of the Jewish Defense League, a New York-based organization that seeks to protect Jews against anti-Semitism, and which the FBI regards as a “right-wing extremist group” for its violent tactics. The JDL provided Ruthless with bodyguards. Before long there were “Israeli soldiers wielding Uzi machine guns at the office,” wrote S. Leigh Savidge, a filmmaker who visited the Ruthless headquarters in this period.

In 1997 the FBI began a two-year investigation into the JD, which they suspected was extorting rappers, including Eazy and Tupac Shakur. The alleged scam went like this: Someone would make death threats to the artists, and then someone else — with whom they were in cahoots — would offer to protect the artists, for $50,000 or so, at which time they’d be taken to a safe spot until a “deal” could be worked out with the perpetrators of the threat. The FBI closed the case without filing charges, and the JDL’s spokesman Irv Rubin stated in a press release that “there was nothing but a close, tight relationship” between the organization and Eazy-E. (170-171) When Eazy tried to get the decision overturned, mayor Omar Bradley responded with a lecture…Then for good measure he threw in some anti-Semitism. “I won’t name the specific racial group that’s using you, brother, but they are destroying us and having a lunch and a bar mitzvah at the same time,” Bradley shouted. “And we know from history that the minute they get finished making money off of you, you’ll be sitting beside Mike Tyson [in prison.” (p. 236) Curiosity was one of his defining traits. Eazy was fascinated by Judaism, for one; he’d stuck with Jerry Heller despite countless anti-Semitic insults, and at his newphew Terry Heller’s grandfather’s funeral, Eazy wore a yarmulke. Tracy Jenargin was Jewish, and said the faith was “very prevalent” in her relationship with Eazy. He even signed a group called Blood of Abraham, a pair of early-twenty-something Jewish kids from the Valley. Though major labels expressed interest, Eazy promised them freedom to express their political messages, onsongs like “Niggaz and Jews (Some Say Kikes).” “He said, ‘You guys are on a militant trip,’” said group member Benyad. “You can talk whatever shit you fuckin’ want.” (p.265) It’s impossible to know if Woods-Wright has done, with his estate what Eazy would have wanted her to. Wright wishes the company had been passed to Heller. “As a Jew, as a white man, he would have handled business,” he said. (p. 288) “Puffy was accused of worse than just having protection on his mind. On the 1995 Southern California trip, in an Anaheim hotel suite, he told a roomful of Crips he’d “give us anything for them dudes’ heads,” referring to Tupac and Suge, a Southside Crip named Keffe D told investigators. Keffe D further maintained that, later at Greenblatt’s Deli in West Hollywood, Puffy clarified his offer:$1 million to murder Tupac and Suge. (p. 316)

Owing to a history of anti-Semitic remarks, Louis Farrakhan gets little respect in the mainstream media. The Nation of Islam leader has long maintained unrivaled admiration throughout the hip-hop community, however. (P. 365)