On my first trip to the International Space Station, I was invited on a mission to Venus. Reluctantly I accepted, not realizing the round trip would take over six months. Oh well; one of the crew, Morty, was also a bridge player, so we occupied our spare time with bidding practice. Little did I realize how fortuitous this would be, and I don’t mean as a puzzle source but financially.
Upon entering the Venusian gravitational field we encountered another spacecraft, and after establishing radio contact it requested permission to dock. Oh dear! At first we were all suspicious, fearing we might perish, but when Mission Control gave us the option, we voted unanimously to take the chance for the benefit of science. A wise decision.
Welcome aboard! Eek and Meek, from Ishtar Terra, were quite familiar with Earth and even some of our games, like chess and bridge. Delighted by the latter, Morty and I asked if they’d like to play a round for fun. “Negk!” came the reply, as they would only play for a venk a point, and by their rules. We had no idea what a ‘venk’ was but agreed. Their scoring was like our Chicago style, but a round was just three deals, honors did not exist, and the vulnerability was decided by venk toss. Whatever; 160 million miles from home we couldn’t be picky.
Luck went our way, as Morty and I made a contract on each deal. Poor Eek and Meek were unhappy, but after the round they honored their agreement, paying us almost a billion venks apiece! Say what? It turns out that under Venusian rules, scores are multiplied instead of added. Wow! Scary to think we could have lost beyond belief, though they might have had trouble collecting.
As a newly ordained venkabillionnaire, well almost, I expect to retire soon but still don’t know what it’s worth in dollars. Please, somebody, help me before I lose my mind! Or maybe that’s happened already.
How close can you come to winning a billion — without going over?
The venk toss has been made, so the vulnerabilities are set. Your side must declare each deal. Enter the contract level and strain (e.g., 3N), risk (UXR) and the number of tricks won (7-13), all of which must be unique. Click Verify to check your Venusian score, which must be over 999 million and under a billion to succeed (scoring 1 billion exactly is impossible). In case you’re wondering, the product of two minus scores does not become positive but just multiplies the amounts lost.
This puzzle contest, designated “June 2018” for reference, was open for over a year. Participants were limited to one try, unlike my usual contests that allowed entries to be revised with only the latest one counting. There were 17 correct solutions (over 999 million but less than a billion) of which 11 achieved the optimal total of 999,999,000.
Congratulations to Grant Peacock, who was the first “almost venkabillionnaire” in the clubhouse. Grant is a clever solver, especially when related to mathematics (as this puzzle) and a good sport with my inane remarks of his NBC affiliation and plumage. (To be sure, I consider him a fine, feathered friend.) Grant’s previous wins include Keep the Ship Afloat, Ever More, St. Valentine's Hand and Victory Celebration.
Ties in the ranking are broken by date and time of entry.
All products must end in 000, so 999,999,000 must be the closest if a billion is impossible. Prime factors of 999,999 are [37,13,11,7,3,3,3] so the goal is to combine them into three legal bridge scores (divided by 10) having unique properties. Trial and error shows three combinations that work: 7 × 3 × 3 = 63 (3 NT+1 Vul 630); 13 × 11 = 143 (1 ××+6 NV 1430); 37 × 3 = 111 (4 ×+2 Vul 1110). Verification: 630 × 1430 × 1110 = 999,999,000.
Tina Denlee: The only perfect solution is 3 NT+1 Vul 630, 1 ××+6 NV 1430 and 4 ×+2 Vul 1110, except you can swap the minor suits, or Deals 1 and 3.
Dan Baker: 3 NT+1 Vul 630, 1 ××+6 NV 1430, 4 ×+2 Vul 1110. Since all bridge scores end in zero, an obvious starting point is 999,900,000 = 990 × 1010 × 1000 (4 ×+1, 6 +1, 3N××=). I wrote a quick script to generate factorizations of 999,901 through 999,999 and looked for combinations of three valid scores. Most have a prime factor too large, and many of those that qualify were tripped up by the vulnerability or uniqueness restriction; e.g., 999,922,000 = 430 × 1510 × 1540 (1 ××+1 NV, 7 = NV, 6 × Vul) requires two NV deals. Besides the ultimate score, the only one I found better than 999,900,000 that meets the restrictions is 999,936,000 = 1860 × 420 × 1280 (6 ×+1, 4 =, 2 NT××+1).
Charles Blair: Your data file of Bridge Result Scores was very helpful.
Grant Peacock: Factoring numbers is right up my alley. Thanks Richard!
Tina Denlee: I guess this could totally happen in the Ishtarian bidding system!
Jean-Baptiste Courtois: Good thing you brought a scoring table on the journey, and your ship had prime factorization technology.
Richard Stein: Hopefully this will land me closer to the top than Pay No Taxes!, which I did quickly and sloppily.
Well, it did by rank, but closer to the bottom by percentile. No problem! Pay your taxes in venks, and the Feds will be none the wiser.
© 2018 Richard Pavlicek