Josh Simons and Na Zhang

At the recent RADIO conference, engineers were challenged to create mathematical expressions for each number from 1 to 100 using only the digits in ‘1998’ (the year VMware was founded) combined with mathematical operators of their choice.

What follows is the summary of the event that was shared with attendees.

Thank you for participating in the RADIO MathWall competition last week! You submitted almost 2,500 expressions, which we have evaluated to present these results. Prizes have been awarded to the members of the winning team and also to two individuals whose contributions caught our attention.

1 Results

We were delighted by the creativity you showed in this competition: the variety of solutions you submitted for each number was impressive. For example, for the number ‘17’ we received the following solutions:

Some of you got creative at the operator level, which can be seen with the use of the remainder operator (%) above. We also saw encountered bit-shift ($9<<1$), summation ($\sum{9}$), matrix multiplication, and combination ($\binom{9}{8-1}$). And while we expected you to concatenate digits to make larger numbers (‘98’), we were surprised to see use of decimal points (‘9.8’), which was an excellent idea.

We also saw some impressive organizational approaches as captured in Figure 1, including someone who built a spreadsheet to track their team submissions as well as a number of people who generated lists of solutions that they later transcribed onto Post-it notes.

Figure 1: Organizational approaches

In terms of your submissions overall, it might have been true that finding solutions for some numbers was significantly more difficult than for others, but the data in Figure 2 show good response rates for all numbers.

Figure 2: The number of correct submissions for each number, 1-100.

2 Prize Winners

All prizes will be mailed to winners over the coming weeks.

Team CA won the competition with an outstanding 95 correct submissions (and zero incorrect or duplicated submissions, both of which were notable feats as well). Congratulations, Team CA! The final scores for all teams can be seen in Figure 3 and the scores for the top 18 teams are listed in Table 1.

Table 1: Top 18 team scores

Figure 3: List of teams, sorted by final score.

In addition to the team prize, we are also awarding two individual prizes to recognize two innovators who embraced and then transcended the mathematics with their solutions.

The first goes to Mahmut, who works on SDDCaaS in Palo Alto. He posted several eye-catching solutions, two of which are shown in Figure 4. It was his ‘80 minutes in traffic’ submission – with square roots as vehicles and double factorials as wheels – that secured him the prize. We didn’t even mind that he used the floor function. 🙂

(a) Rooting around…                          (b) It’s an expression AND a cartoon

Figure 4: Two of Mahmut’s submissions

Not to be out-done, Viji from the vSAN team submitted an expression that evaluates to the same number regardless of whether it is read right-side up or upside down, as shown in Figure 5. Cool!

(a) Rightside up                                             (b) Upside down

Figure 5: Viji’s submission

3 Acknowledgements

Many thanks to the anonymous attendee who added the Post-it shown below to the MathWall. In the midst of checking 2500 math expressions this afforded us a welcome and very fun break!