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Self-contained math crossword with if-then-else clues

Puzzling Asked on March 30, 2021

An entry in Fortnightly Topic Challenge #43: Variety Crossword Grids


Since I’m not good with with words and crosswords, here is a math crosswords: to know all the operands for the calculations you will have to replace the content of the brackets (e.g. {1 across}) with the answer to that clue (e.g. the answer to 1 across).

Some clues are of the form "if condition then A else B". As you can easily imagine in this case the answer is A if the condition is true and B otherwise.

grid

ACROSS

1: 2 to the {26 down}
5: if {27 across} is prime then 243 else 148
7: if {11 down} is a multiple of 42 then 300 else 118
8: if {1 across} < {35 across} then 47 else 82
10: if {33 down} is prime then 1848 else 2949
13: {31 across} + {7 across} + 176
15: {13 across}/{5 down}
16: {10 across} x {28 across} + 16837
18: {8 across}th pentagonal number
20: product of the digits of {31 across}
21: {32 across} – {4 down}
22: 6th term of OEIS A{9 down}
23: 7 x {4 down} / 10
24: 1000 + {5 across}
26: 5 x {20 across}
27: {30 across} + {13 across} – 664
28: if {2 down} is a multiple of 3 then 1567 else 1887
30: if all the digits of {1 down} are even then 1779 else 1189
31: {4 down} – 4
32: 2 x {23 across}
34: {28 down} / 5
35: {32 across} * {27 across} + 252

DOWN

1: 3226 x {17 down}
2: 2 + {13 across}
3: 520 + {24 down} * {20 across}
4: 2 * {20 across}
5: {33 down} read backwards
6: 4 x {30 across}
9: 4 x {3 down} + 140
11: {30 across} – 307
12: if {32 across}<50 then 8532 else 4137
14: ({15 across} – 5)th fibonacci number
17: if {26 across} is a multiple of 30 then 205 else 285
19: if {9 down} is odd then 27243 else 97158
24: if {14 down} is prime then 2896 else 1010
25: if {13 across} is a multiple of 3 then 4881 else 4798
26: {34 across} – {5 down}
27: {20 across}th prime number
28: {7 across} / 2
29: 12 x {8 across}
33: {30 across} – {24 across}

SOME CLARIFICATIONS

  • All the answers are natural numbers in base ten without leading zeroes.
  • Fibonacci numbers start with zero: 0, 1, 1, 2, 3, 5….
  • Here you can find the OEIS website.


source: original puzzle by me. For this reason can you please provide some feedback about the grid? Is it too easy?

4 Answers

Steps:

That should be enough to get anyone started - It's pretty much substitution from then on.

Grid at this stage:

At this point, I went through the clues, and put in all values I knew. Then it was pretty much a top to bottom substitute and Calculate.

Across

Grid after across substitutions:

Then onto the down clues:

Finishing Up:

Which leaves us with:

2 remaining clues are look ups which I include for completeness and final correctness check.

Correct answer by Chris Cudmore on March 30, 2021

Was fun to solve it!

Here is my solution:

Answered by npkllr on March 30, 2021

Here's a start:

Illustrations are hard work. Feel free to copy https://docs.google.com/spreadsheets/d/1VbSrX8qcxtUp84aeYh01qklIHDrPhQX230_i8Gt-5xA/edit?usp=sharing and amend. Here is the state of affairs after the first few steps:

Answered by chx on March 30, 2021

without any difficulty you can figure out

across

24 first digit is known because you are adding a 3 digit number to 1000 so the first digit has to be a one

28 last digit is known because both number share the same digit

30 last digit is known because both number share the same digit

down

17 last digit is known

19 second digit is known

knowing 24 across first digit you know 24 down is 1010

14 across can be figure out using the 7 from 28 across and the length to find only value in sequence to give you that.

from there you also know 15 across

these are just a few quick ways to get started on this puzzle

Knowing the last digit of 30 across tells you 25 down

Answered by Styxsksu on March 30, 2021

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