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19 Mar 2026, 19:56
Kudos
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We have a five-digit address d1 d2 d3 d4 d5 with three constraints:
Myrna: d1 + d2 = d3, and d4 + d5 = d3
Deon: d3 divides evenly into the two-digit number d1d2, and also into d4d5
Kermit: digits increase from d1 to d3, then decrease from d3 to d5 (d1 < d2 < d3 > d4 > d5)
Step 1: Find d3.
Since d1 + d2 = d3, d1 < d2 < d3, and d1 >= 1 (it's the leading digit), the maximum d3 can be is 9. Let's test d3 = 9.
Possible (d1, d2) pairs where d1 + d2 = 9 and d1 < d2 < 9: (1,8), (2,7), (3,6), (4,5).
Now check Deon's divisibility rule — 9 must divide 10*d1 + d2:
- 18 / 9 = 2 (works)
- 27 / 9 = 3 (works)
- 36 / 9 = 4 (works)
- 45 / 9 = 5 (works)
All four pass! For any other value of d3 (like 8, 7, 6, etc.), Deon's divisibility rule fails for every valid pair — you can verify this. So d3 = 9 is the only possibility.
Step 2: Find d4 and d5.
We need d4 + d5 = 9, d4 > d5, d4 < 9, and 9 must divide 10*d4 + d5. The candidates are (8,1), (7,2), (6,3), (5,4) — all pass the divisibility test.
But we must pick from the available options: {0, 3, 4, 5, 7, 8}.
- (8,1): d5 = 1 is NOT available
- (7,2): d5 = 2 is NOT available
- (6,3): d4 = 6 is NOT available
- (5,4): d4 = 5 is available, d5 = 4 is available — this works!
Finally, check uniqueness: with d4 = 5 and d5 = 4, we can use (d1, d2) = (1,8), (2,7), or (3,6) — all giving five unique digits. The pair (4,5) is excluded since 5 and 4 are already taken.
Answer: Fourth Digit = 5 (A), Fifth Digit = 4 (B)
Myrna: d1 + d2 = d3, and d4 + d5 = d3
Deon: d3 divides evenly into the two-digit number d1d2, and also into d4d5
Kermit: digits increase from d1 to d3, then decrease from d3 to d5 (d1 < d2 < d3 > d4 > d5)
Step 1: Find d3.
Since d1 + d2 = d3, d1 < d2 < d3, and d1 >= 1 (it's the leading digit), the maximum d3 can be is 9. Let's test d3 = 9.
Possible (d1, d2) pairs where d1 + d2 = 9 and d1 < d2 < 9: (1,8), (2,7), (3,6), (4,5).
Now check Deon's divisibility rule — 9 must divide 10*d1 + d2:
- 18 / 9 = 2 (works)
- 27 / 9 = 3 (works)
- 36 / 9 = 4 (works)
- 45 / 9 = 5 (works)
All four pass! For any other value of d3 (like 8, 7, 6, etc.), Deon's divisibility rule fails for every valid pair — you can verify this. So d3 = 9 is the only possibility.
Step 2: Find d4 and d5.
We need d4 + d5 = 9, d4 > d5, d4 < 9, and 9 must divide 10*d4 + d5. The candidates are (8,1), (7,2), (6,3), (5,4) — all pass the divisibility test.
But we must pick from the available options: {0, 3, 4, 5, 7, 8}.
- (8,1): d5 = 1 is NOT available
- (7,2): d5 = 2 is NOT available
- (6,3): d4 = 6 is NOT available
- (5,4): d4 = 5 is available, d5 = 4 is available — this works!
Finally, check uniqueness: with d4 = 5 and d5 = 4, we can use (d1, d2) = (1,8), (2,7), or (3,6) — all giving five unique digits. The pair (4,5) is excluded since 5 and 4 are already taken.
Answer: Fourth Digit = 5 (A), Fifth Digit = 4 (B)
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