Puzzle 8K35   Main

The Bricks of Amenhotep

by Richard Pavlicek

Few people are aware that Pharaoh Amenhotep IV (18th Dynasty) invented the high-card ranks inherent to bridge and other card games. Fortunately, PavCo Historians are here to educate you, so read on.

In the palace of Amenhotep IV were 16 bricks of four different sizes. Etched on each large brick was a circle depicting the sun god Aten; the second largest bricks had etchings of Amenhotep I to IV; the third largest, their four wives; and the smallest, their four sons. Logically these brick ranks evolved into ace, king, queen, jack, as familiar today.

Every year Amenhotep IV would waive taxation to any landowner who could arrange the bricks in a diagram to satisfy his cryptic whim. Below is one such waiver, translated from hieroglyphics:

With southerly instigation, and shovels in control, hands along the Nile must render oppositional forces brickless. Landlords, place your bricks among the pawns! -Amenhotep IV

Pawn layout (add 16 bricks)	2 3 — —
— — 3 2			— 2 — 3
Form 1040-A © 1339 BC	3 — 2 —

PavCo Historians interpret the ancient wording to mean:

Distribute the 16 high cards (A-K-Q-J) so North-South can win all six tricks with spades trump and South to lead.

Many solutions exist. Your goal is to accomplish it with (1) fewest N-S HCP, (2) fewest South HCP, and (3) fewest West HCP, in that order of priority. Further, to qualify as a legal bridge ending, at least three suit holdings must remain void.

Tim Broeken Wins

In May 2011 this puzzle was presented as a contest, with 84 participants from 24 locations. Thanks to all who entered, and congratulations to the 18 who found the optimal solution, and the 13 others who came close. Solvers are ranked by the fewest HCP (N-S, South, and West in that priority) with remaining ties broeken, er broken, by date-time of entry.

Kudos to Tim Broeken, the first solver in the brick yard, as well as the first double winner in this contest series. Do you suppose he bought his bricks at the Yarborough Fair?

Winner List

Rank	Name	Location	N-S	S	W
1	Tim Broeken	Netherlands	14	5	12
2	Zla Khadgar	Ohio	14	5	12
3	Charles Blair	Illinois	14	5	12
4	Edouard Bonnet	France	14	5	12
5	Reint Ostendorf	Netherlands	14	5	12
6	Gareth Birdsall	England	14	5	12
7	David Brooks	Australia	14	5	12
8	Dan Dang	British Columbia	14	5	12
9	Audrey Kueh	England	14	5	12
10	Jonathan Mestel	England	14	5	12
11	Hendrik Nigul	Estonia	14	5	12
12	Jonathan Buss	Ontario	14	5	12
13	Simon Creasey	England	14	5	12
14	Pavel Striz	Czech Republic	14	5	12
15	Ufuk Cotuk	England	14	5	12
16	Julian Wightwick	England	14	5	12
17	James Lawrence	England	14	5	12
18	Nick Jacob	New Zealand	14	5	12
19	Alberto Gioa	Italy	14	5	13
20	Dan Baker	Texas	14	5	13
21	Jeffrey Tsang	Pennsylvania	14	5	13
22	Jacco Hop	Netherlands	14	8	11
23	Radu Vasilescu	Pennsylvania	14	8	11
24	John Reardon	England	14	8	12
25	Paul Nelson	California	14	8	12
26	Thomas Haukland	Norway	15	5	10
27	Jon Greiman	Illinois	15	5	10
28	Jonathan Ferguson	Texas	15	6	12
29	Jim Munday	California	15	7	10
30	Colin Schloss	Pennsylvania	15	7	10
31	Richard Stein	California	15	8	13

Puzzle 8K35   Main

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Solution

A change of pace, as this amenipotent challenge seems more like Sudoku than bridge; but then, bridge wasn’t invented yet. The Origin of Bridge came 22 years later thanks to Amenhotep IV’s son, better known as Tutankhamun. (Not all historians agree, but that’s my story and I’m stickin’ to it.) Indeed, some people were disappointed that the solution was based on a crossruff, rather than some amenruffensqueeze. To them, I will point out that we’re talkin’ bricks here, not precious gems.

The condition of “at least three voids” has no bearing on the solution, as any construction with two or fewer voids, besides being illegal* would require more HCP for North-South to win six tricks. For example, with two voids the minimum is 16 HCP.

*Legal endings must be reachable from a full deal without a revoke or other irregularity. While hardly required for puzzles, especially about bricks, I try to keep things legal so I might pass for a bridge player in a dimly lit room.

The most obvious requirement is that N-S have the A, as even the High Priest of Amun couldn’t avoid that loser; further, it should go to North to minimize South’s HCP. The next idea might be to give East-West each a mummy, er stiff, K or Q. Several solvers tried this on early attempts but found improvements, so I’ll attribute my first example to Kharis, the most feared mummy of all time:

win all Success	A 2 K Q J 3 — —			Trick 1 S 2 N	Lead 3 K	2nd Q A	3rd A J	4th K 2	W-L W1 W2
Q — K 3 K Q 2			K A 2 A A 3
South leads	J 3 — Q J 2 J				North wins the rest

The above HCP counts of 15:5:10 for NS:S:W total one point fewer than the winning solution of 14:5:12, but of course lose out in the stipulated priority.

Norwegian wood

Another way of achieving the 15:5:10 HCP counts is to give North-South all the trumps and minimal HCP elsewhere. Thomas Haukland (Norway) put it all together for a simple crossruff:

win all Success	A K 2 Q J 3 — —			Trick 1 S 2 N	Lead 2 3	2nd 3 2	3rd 2 3	4th K K	W-L W1 W2
— K Q 3 K Q 2			— A 2 A K A 3
South leads	Q J 3 — J 2 J				Crossruff the rest

Declarer could even succeed in the above layout if he led a trump to dummy.

Jim Munday: Even Fritz could bring this one home. If I find the correct solution can you waive taxation for me this year?

Of course! Open an account in PavCo Cayman Bank and you will Pay No Taxes!

Bricklaying by the numbers

In theory, the minimum HCP for N-S is 14, since the A must be held, and the weakest the remaining honors can be is three queens and four jacks. South’s theoretical minimum is 5 HCP, because 4 HCP (four jacks) would mean no void suit, demanding at least 16 HCP for N-S. The remaining high cards dictate West’s theoretical minimum as 11 (three kings and a queen) which, alas, cannot be achieved. West must settle for 12 HCP, as Tim Broeken (Netherlands) shows with his winning entry:

win all Success	A Q 2 Q J 3 — —			Trick 1 S 2 N 3 S 4 N 5 S	Lead 2 3 J J Q	2nd 3 2 2 3 ?	3rd 2 3 Q J	4th K K A A	W-L W1 W2 W3 W4
K A K 3 Q 2			— 2 A K A K 3
South leads	J 3 — Q J 2 J				Win the rest

West has no effective defense as declarer crossruffs. If he pitches a heart on the second diamond preparing to overruff, the North hand becomes high and the last trump is drawn. If he pitches a club (as shown), South safely ruffs a heart to establish the Q. South next leads the good Q, and West can only choose which red queen will win a trick.

Charles Blair: According to Geza Ottlik, West is squeezed in hearts on the second round of diamonds.

I have a theory about this too. The Great Pyramid is located in Giza, which translates to Geza in Hungarian. Trust me, when Ottlik penned Adventures in Card Play, he was high on tana leaves.

The optimal solution (14:5:12) discovered by the top 18 solvers is unique, and so proved by combinatorial exhaustion.

Mission Control

Jonathan Mestel: Ra, Ra, PavCo! I was hoping for a sacred crocodile coup.

Wayne Somerville: How did King Amenhotep manage to get a copyright in 1339 BC? How did they even know it was 1339 BC?

Kharis? We have a new mission. An infidel dares to question our veracity. [Richard prepares the fluid of nine tana leaves]

Puzzle 8K35   Main

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© 2011 Richard Pavlicek