I Read You 5x5Logic puzzles require you to think. You will have to be logical in your reasoning.
"Congratulations, Great-Aunt Nora!" The voice of Victor Summ, her eldest nephew, was tired, but exultant. Her older sister was the first grandparent among the five Shekrie siblings.
"Let me put you on speaker-phone, Vic. Corman is here." Nora had little doubt that her romance with a math teacher was the reason Victor, a research statistician, called personally, instead of letting his mother handle the news.
Nora beamed at Corman as she hit the button. "You're on, 'Daddy'. Mother and children are doing fine?"
"Cogita's doing great, although we had a bit of a shuffle in the maternity ward. Hi, Professor diNoni -- you'll love this one."
"Hi, Victor. I've heard more about you than ... no, you've known your aunt longer. You probably know how much she's talked about you."
"It runs in the family," he smiled across two time zones. "Doc Matter, our OB, said it was the strangest coincidence she's seen in a decade. The kids were born 10, 20, 30, minutes apart, up to an interval of an hour-fifty ..." Vic's voice trailed off.
"Except for one interval?" Corman filled in.
"Right. She said it was really weird, watching the time. She said Adele was born at six sharp, Brand at 6:10, and they just kept hitting 10-minute multiples, until Elana came out at 7:50."
Nora yelped. "You had *eleven*," then her left brain caught up, "no, just the quintuplets. Sorry."
"De nada, Aunt Nora. But that's where the problems started: they had the birth order mixed up. Someone had assumed we'd named them in order, with Brand, Caleb, and Derec in between. I pointed out that they'd managed to get all five wrong, and then Cogita wanted me."
"So they got it sorted out?"
"Not quite. The OB saw to the post-delivery stuff while we beamed at each other. Then a nurse came in and said they figured it out: we'd named them in alphabetical order, but by the last letter of their names. They had all five wrong again! Heck, even if we'd done it in reverse alphabetical order, either way, they would have had all five wrong!"
"So what did they do?"
"Doc Matter said she may be getting gray, but she wasn't going to sign the certificates until they were all correct. She dictated the birth times and told them to match them with the weight and length stats to sort things out -- and if they couldn't, they shouldn't bother reporting for work after tonight."
He took a cleansing breath. "On a happier note, we'd like the blood aunts and uncles to serve as godparents, since there are five of you. Would you stand for Caleb, Aunt Nora, since the two of you have the same birth position in the family?"
"I'd love to. And if anyone in this family declines, I'll have Corman make them figure out the birth order. Do you have it yet, dear?"
Vic broke in, "He doesn't have enough information yet, and I can hear you smirking at him."
Corman held up a hand to keep her quiet. "Since I don't know much about Nora's birth order, I'll have to make this a bigger question. How far apart were Brand and Elena born?"
"Fifty minutes, on their cute little noses."
"Got it." Corman recited the birth order, complete with times. Can you do the same?
HintThere is only one way (plus a mirror-image reflection) to arrange ten different intervals in a span of 11 ten-minute units. If you need help, search for "Optimal Rulers".
6:10 Adele 0:10 later
6:40 Brand 0:30 later, 0:40 after Derec
7:30 Elena 0:50 later, 1:30 after Derec, 1:20 after Adele
7:50 Caleb 0:20 later, 1:50 after Derek, 1:40 after Adele, 1:10 after Brand.
The missing interval is one hour.
Number the ten time points from 0 to 11 (6:00 to 7:50). The only ways to arrange them to get ten different intervals for the births are events at points 0, 1, 4, 9, and 11 and the reverse: 11, 10, 7, 2, and 0. The clue gives three birth times at 6:00, 6:10, and 7:50, so we have the first arrangement.
The clues about alphabetic and reverse-alphabetic order giving five wrong placements mean that Caleb and Derek were not born 2nd, 3rd, or 4th; Adele and Elena were not born first or last, and Brand was not born 2nd or 4th.
The 50-minute interval given at the end means puts Brand and Elena into the 3rd & 4th spots, which leaves 2nd as the place for Adele.
Finally, we have Caleb and Derec to fill the first and last spots. Caleb and Nora share a birth position. The first paragraph mentions that Cogita is Nora's older sister, so Caleb cannot be the firstborn.
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