Heading for the beach
The other day I took a ride to the beach with a friend of mine. Part of our conversation follows.
- I know that one and six is six. But, is two and five 10?, he asked.
- Not at all, I replied, two and five is twelve.
- Really? Then what is 3 and 3?, he asked.
- Seventeen, I answered.
- Ah, I think I get it now, he said.
What were we talking about?
Problem source: Car Talk.
November 27th, 2007 at 11:22 am
I’m curious… any ideas here?
The first and second clues are consistent with a base 8 numbering system but not the third clue. I can’t come up with any geometric explanation of these answers either.
November 27th, 2007 at 2:39 pm
Hopefully somebody will crack it.
November 27th, 2007 at 6:00 pm
Maybe the answer is the following:
1 6 is 6
now we add and substract 1, so 1+1 = 2 and 6-1 =five
and the result is 6+6 =12.
So if we do teh same again, add and substract 1:
2+1=3; 5-1=4
so 3 and 4 would give us six more, so eighteen 18, but we have 3 instead of four so the result is 18-1=17.
Does this make sense?
November 28th, 2007 at 5:09 am
Hmmm… what can we force this into?
ax+by+c=z
a+6b+c=6
2a+5b+c=12
3a+3b+c=17
Solving for a, b, and c, …
(line 2 – line 1)
a-b=6
(line 3 – line 2)
a-2b=5
b=1
a=7
c=-7
So, if one wants an inelegant solution, f(x,y) = 7x+y-7
November 28th, 2007 at 3:49 pm
Ah…
2 and 1 is 8!
3 and 1 is 15!
Yes, I know the answer but I’m not telling. Those, however, are a couple of solid hints.
November 28th, 2007 at 3:51 pm
Oh, by the way.
The exclamation points in my previous post are just that. Not notation for 8 factorial or 15 factorial.
November 28th, 2007 at 4:31 pm
Tomorrowist’s solution works with Nick’s hints.
Perhaps, however, we would rather say …
First number, minus one, then times seven, then plus the second number
or
(X-1)7 + Y
November 28th, 2007 at 4:43 pm
Ole has arrived at a simple math formula and it works.
Another hint: Neither X or Y are zero. X is <=3 Y is <= to 7.
The question remains, what were they talking about during their ride to the beach?
November 29th, 2007 at 1:52 am
Ah, now I get it. On this, the third day of the first week of the posting of this problem.
On what day of the posting of the problem is that, you ask? Well, just subtract one from the week number, multiply by 7, and add the day number; that gives you the overall day number. Or, more inelegantly, multiply the week number by 7, add the day number, and subtract 7.
Coming back in two weeks? That would be the third day of the third week, or the 17th day overall.
November 29th, 2007 at 3:23 pm
Tomorrowist,
Extend your arms out to the side as far as you can. From the fingertips of your left had to the fingertips of your right hand is a small indication of by how much you missed it.
Nick
October 12th, 2009 at 7:56 am
Were they were talking about bicycle gear ratio selection?