Myself and Mrs D hiked up a mountain whilst we were in the Rockies this summer. Well, we hiked up several, but we’ll just stick with this specific one !
Going uphill we managed a rock steady one and a half miles per hour. Coming back down we achieved a staggering four and a half miles per hour. The round trip took us six hours.
How far was it from the start to the top of the mountain ? (or from the top to the bottom !)
Hi Mike, your answer suggests six hours to cover two miles (one mile there and another mile back )?
You’re going to have to give this one another look Mike - sorry.
PS. just to avoid any angst, there are no silly tricks. The walk could well have been along a dead level canal, but I would then have to invent a different story to justify the speed difference outbound and inbound !
For the seventh domino (2-2 given plus 5 already identified above) I could see two possible locations for “0-0”. these are shown in Green and Blue below.
If I selected the Blue one, it would deny me using either of the 4-0 or 0-4 options associated with those Zeros. I couldn’t see any other 0-4 or 4-0 pairs available.
I therefore selected the 0-0 domino shown in Green below.
Now I had to choose between upper 4-0 or the lower 0-4 just the the right of the given 2-2.
Whichever option I chose, would mean the other option must NOT form a domino (you can’t have two 4-0 dominoes in a set) and as a consequence, would force the pairings of quite few dominoes in that “eastern” arm of the layout.
Having selected the upper version of domino 4-0, the 3-1 followed. then the 0-3 (otherwise there would be two 4-0’s !) The 5-2 and 4-6 were also forced to avoid orphans and doing so, eliminated a possible 2-3.
The 2-3 (above the given 2-2) was next simply because the only other 2-3 had just been eliminated. The 5-6 followed to avoid orphans !
Of the tiles that were left, I could only find one pair that would make a unique domino. All the other tiles could make at least two versions of the outstanding dominoes.
The unique pair of tiles made the 2-4 domino, shown in Blue.
This allowed me to subsequently pair up tiles to form another half dozen dominoes.
Divide 45 into four parts, such that the first part plus two, the second part minus two, the third part multiplied by two, and the fourth part divided by two all equal each other.
8,12,5,20
I realised that I needed a root number which all the sums equalled, call it x and the 4 parts a,b,c,d
A+2=x
B-2=x
C2=x
D/2=x
Thus, A+B=2x, C=x/2, D=2x.
A+B+C+D=45, and also from above = 2x +x/2 + 2*x = 4.5x.
Therefore X=10.