[True or False Quizes]

DeGe's solution shows that {Mike and the North girl}

can be interchanged with {Paul and the Fisher youngster},

whose wrong answers can be either {7 0} and {3 4}

or v.v, respectively.

From what I remember while solving it, there were no unresolved elements and each piece fitted in one place only (I have now deleted the file that I used to work this out).

The interchangeability between Mike/North and Paul/Fisher is also resolved. I don't remember how exactly I resolved it but it had something to do with there being only 3 girls names... Grace, Karen, and Dot. In case of interchanging Paul/Fisher and Mike/North, some other condition was being violated.

[Nines Clock]

[double game]

E 18

J 10
L 66
S 34

[Synchronizing clock]

Ask the server for time. Let us say you sent the request at time T; this request reaches the server at time T+t1. The server sends the time T+t1.
So, you get the time T+t1, but the actual time now is T+t1+t2 when you get the time.

Program such that you send another request at the very instant you get the first response from the server.

So, at time T+t1+t2, you send the second request, and the time you receive from the server is T+2t1+t2 while the actual time is T+2t1+2t2 when you get this time.

Calculate the difference between the two times recieved. You now know how much is t1+t2.

Now, ask the server to send to send you the time (Tn) exactly n seconds later; for example you ask the server what time will it be after 30 seconds.

As before, you will get the time Tn+t1, when the actual time is Tn+t1+t2.

Subtract t1+t2 from the time Tn+t1 received from the server and set your computer clock to Tn after n seconds.

[True or False Quizes]

Here's what I got

[Summing a summed sequence]

i see the error. Dont have time now but will correct it later

[Another spin on a classic: Transporting Apples]

The problem statement says

• "His truck can only hold 1000 apples."

​the update says that the store is 1000 miles away

If the driver starts with a full load [1000 apples] and drives 1000 miles, he will have 0 apples left upon arrival.

Thus, unless he can ferry apples to some point(s) in between and then move these forward, there is no way to every deliver even 1 apple.

If we assume that there is a point halfway [500 miles] then he could do the following:

• leave the warehouse with 1000 apples
• drive 500 miles [now has 500 apples]
• leave the apples at the halfway point [now has 500 apples]
• drive back to the ware house
• leave the warehouse with 1000 apples
• drive 500 miles [now has 500 apples]
• Picks up 500 the apples at the halfway point [now has 1000 apples in the truck and 0 apples at the halfway point]]
• Drives the remaining 500 miles to the store and delivers 500 apples

Thus for 2 trips[500 and 1000 miles one way (3000 miles total round trip)] 500 apples can be delivered

to deliver 3000 apples would require:

• an interim storage area at 500 miles
• 6 "short" round trips between the warehouse and the interim storage area [1000 miles R/T each]
• 6 "long" round trips from the warehouse [stopping at the interim storage area to reload] to the store [2000 miles R/T each]

Notes:

• you can break this up many ways
• it is not clear what the optimal interim storage area distance [from the ware house] is [and if more than 1 helps]

Yes, but for returning also he would need to eat apples

So, if he goes 500KM, he would eat 500 while going and 500 while coming back.

533

[Summing a summed sequence]

Each digit repeats itself in each position as follows:

in ones position 1000 times

in tens position 100 times

in hundreds position 10 times

in 1000 position 1 times

and 1 appears once in 10 000

Now, 0 + 1 + 2 +3 .... + 9 = 45

So, sum of digits is 45*1000 + 45*100 + 45*10 + 45*1 + 1 = 45*1111 + 1 = 49996