Pizza Contest in Pizza Bay
08/01/2000
Five pizza companies - Andy's, Bebe's, Cassidy's, Denzy's and Elsie's - submitted 5 pizzas each, with toppings of pepperoni, bologna, cheese, anchovies and pineapple, for the Annual Best Pizza Contest held in Pizza Bay. The best pizza in each topping category would get 5 points, the second best 4 points, and so on. There were no ties in any category or in the final total.
Andy's, the winner with 18 points, was 2 points up on Bebe's. The others, in order of merit, were Cassidy's, Denzy's and Elsie's. Each of the 5 took first place in one topping. Andy's was first in pepperoni; Bebe's was first in bologna and third both in cheese and anchovies; Cassidy's was first in cheese, second in pineapple and third in pepperoni; Elsie's, though new to the industry, took first place in pineapple and second place in anchovies.
What was Denzy's mark in each of the 5 toppings?
CrossNumber 54 (All answers are numbers; prime means a prime number.)
Across
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1. 2/3 of (2 Down x 28 Down)
4. 16 Down x 28 Across
7. Prime
8. 16 Down + 10 x 25 Across
10. Prime
11. 15 Across + 4 x 5 Down
12. 5 x (2 Down + 16 Down)
15. Prime
17. 5 Down x 25 Across
18. 10 Across x 26 Down
19. 14 Down + 10 x 26 Down
21. (2 Down x 16 Down)/6
23. 23 Down - 2 x 2 Down
25. 10 Across - 28 Down/4
27. 10 Across + 13 Down
28. 2 Down + 7 Across
29. 2 Down x (10 Across + 16 Down)
30. 9 + 2 Down x 8 Across
Down
1. 7 Across x 10 Across
2. (5 Down + 10 Across)/2
3. 10 Across + 14 Sown
4. Square of 10 Across
5.Prime
6. 10 Across + 8 x 11 Across
9. 5 Down + 15 Down
13. 2 Down x 5 Down
14. (13 Down + 21 Across)/2
15. 13 Down - 16 Down
16. 28 Across + 4 x 25 Across
19. 10 x 19 Across - 2 x 25 Across
20. 7 Across + 3 x 8 Across
22. 6 x 1 Across - 5 x 7 Across
23. Square of 25 Across
24. 10 Across + 15 Down
26. 2 x (7 Across - 10 Across)
28. 7 Across + Square root of 3 Down
Contest Rules: All entries must be received by Aug. 25, 2000. The winners of the word puzzle and CrossNumber (can be the same person) will be drawn from all correct entries. Fax all entries to 847-634-4240. All entries must include name, complete address, company affiliation and daytime phone number in order to be considered. Employees of PennWell and their immediate families, agents contracted by PennWell and their immediate families, employees of PennWell and its subsidiary companies and their immediate families, and members of the Advanced Packaging Advisory Board and their immediate families, are not eligible to compete.
Solutions to May's Think Tank Puzzles...
Grand Prize Winners
Congratulations to our most recent winners: Paul Morgan of K & F Electronics Inc. for Hal's Password, and Gail A. Schooley of The Engineering Consortium Inc. (TEC) for CrossNumber 52.
Hal's Password
Answer: 11859
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Solution: Let the number be "abcde." From the first clue, "c" must be even and the last two digits must be a number greater than 50. Then "a" is 1. From the second clue, "e" is odd.
The 10,000 +1,000b + 100c +10d + e is the number. But 100 + 10b + c = 2(10d + e).
Let the other be X, then 2X2 + 1 = 10,000 + 1,000b + 100c +50 + 5b + c/2; 4X2 = 20,098 + 2,010b + 201c. Thus, "c" is 8 or 4, as any other even digit would not make "e" an odd digit.
Now we have the number as 1b4d7 or 1b8d9. If the number is 1b4d7, 2X2 + 1 ends in 7 and 2X2 ends in 3 or 8, which would not give an integer square root. Hence, 2X2 + 1 is 11859, 13869, 15879 or 19899. Only 11859 gives an integer value of X = 77.