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19.4 Solution, Puzzle, and New Crossword

Vector 20:1, page 35

competitions and puzzles

Transcribed from the printed issue; not yet reviewed. Read it in the PDF of the issue, page 35

Solution to Crossword in 19:4

The completed 12 by 12 crossword grid from Vector 19.4, filled with APL symbols, names and digits; row 1 reads ⌊ / ( V > 0 ) / V, and the bottom row reads 2 / 1 | T and 1 /

Puzzle (from Howard Peelle)

NOW I KNOW

There are two positive integers, each greater than 1 and less than 100.

Pete knows their product. Serena knows their sum. First, Pete says: “I don’t know what they are.” Then Serena says: “I know you don’t know.” Then Pete says: “So, now I know.” And Serena says: “So do I.” What are the two integers?

This problem has been around for a while in various guises and is usually presented in terms of Mr. P (product) and Mr. S (sum).

I have changed the names to Pete and Serena, in reference to two great tennis players. Solution in the next Vector!

New Crossword

The empty 12 by 12 crossword grid, numbered 1 to 38

Across

  1. Where the active workspace came from
  2. Coding and testing are ______ in APL than in other languages
  3. Format the absolute values of the elements in vector X corresponding to 1 bits in vector M
  4. Matrix MAT with vector E as a new rightmost column
  5. Flag distinct elements (first occurrences) in vector VA
  6. Conjugate (imaginary portion is negated) of complex number C (for APL systems with complex number support)
  7. Round elements of RDS to nearest integers (with X.5 down to X)
  8. Do all the elements of V equal IMP?
  9. A times pi
  10. I×DK for scalar I, bit vector DK, without multiplying
  11. RB[5+⍳TN]
  12. Current size of the symbol table
  13. ×/Iρ*1
  14. C[;1]÷C[;2] for two-column matrix C
  15. P=0 for Boolean P
  16. J2L[____] to get J2L in sorted order
  17. ¯15↑1
  18. M[___;] to get M in alphabetic order according to the alphabet A
  19. Name of the ⍕ function
  20. Rank (number of dimensions) of Y
  21. One random number from the set (U×L+1), (U×L+2), (U×L+3),... (U×L+Y)
  22. How good programmers spend the majority of their time

Down

  1. Display VC to W decimal paces
  2. A-S×⌊A÷S
  3. Index in vector IM of its largest number
  4. Elements in vector VRV corresponding to 1s in bit vector D
  5. Flag the first M elements of S that equal -AM
  6. Index in vector SA of 1÷P5
  7. Array of 2s, with shape TT
  8. Vector V with scalar E stuck to its front
  9. Speed, size and __________: the key measures of APL program quality
  10. Flag elements of TOP5 that match scalar XAD
  11. Average across each row of matrix D
  12. Local variables in suspension
  13. Flag leading elements of vector YC that are integers
  14. Area of circle of radius R
  15. (+/KS)ρ5 for integer vector KS
  16. (~B∊M[12+⍳(ρM)-12])/B
  17. Ranking vector for golf scores RLI (1 = lowest score)
  18. Add N to each element of JMM
  19. Product of AO and T
  20. APL is ___ to use
  21. From the set ⍳G, return A distinct random numbers
  22. Length of vector O