Ciphers and Puzzles from Competitors

[10degrees-admin]

NT3 – 25265650

@Kford-academy NT3 – 25265650 incorrect.

[10degrees-admin]

NT3 – let’s try again! 25164150

@Kford-academy NT3 – 25164150 correct (how did you manage to go wrong? Don’t answer.)

One more to do, NT 1. Unless someone else beats you to it. (rating *)

These are still pending an answer by anyone:
TLW A Number To Find__Block 13 #49100 (rating **)
TLW A comPLEXmatrix___Block 13 #49104 (rating ***)

[10degrees-admin]

NT1 – 906609. Is the result of 993*913.

Well done Kford academy that is correct but can you do the same for the first 1000

@Kford-academy NT1 – 906609. Is the result of 993*913. Correct.

@TLW i created a program in 5 minutes to solve NT3 here it is:

def sum_square_difference(n):
numbers = range(1, n+1)
sum_squares = sum(i**2 for i in numbers)
square_sum = sum(numbers)**2
return square_sum – sum_squares

print(sum_square_difference(100))

The value at the bottom is changeable to however many numbers you want to go on for.

@Kford-academy NT1 – 906609. Is the result of 993*913. Correct

@Sankaya Thank you for your little python script.

It can be found by the following mathematical calculation:
(((100*101)/2)^2)-((2*100+1)*(100+1)*100/6) = 25164150

In pyhton it would be:
answer=(((100*101)/2)**2)-((2*100+1)*(100+1)*100/6)
print(answer)

In python setting r1 to range required (here 1000):
r1=1000
r2=r1+1
answer=(((r1*r2)/2)**2)-((2*r1+1)*(r1+1)*r1/6)
print(answer)

250166416500.0

I use the free math package PARI-gp for most of my number theory workings…

\\By program to allow for variable range:
range=100;zum=range*(range+1)/2;zumsq=(2*range+1)*(range+1)*range/6;print(zum^2-zumsq);

\\Program by iteration method:
p=q=0;for(n=1,100,p+=n^2;q+=n);print(q^2-p);

[10degrees-admin]

KA-8 – The Countdown Conundrum

With the numbers 5, 6, 7, 8, 9 and 10, how many three-digit numbers can you make? Note that you can only use the standard four operations (use the symbols + (add), – (minus), * (multiply) and / (divide)), and you can only use each number once. But you do not have to use all of the numbers! To get some sort of idea for what you have to do, I have completed the numbers 100 to 124 for you. And I am going to compile an answers list for when I release ‘The KA Answers – KA-8’! (That will be in parts, for compactness in the forum.)

100=6*(9+8)-7+5
101=6*(10+7)-9+8
102=6*(10+7)
103=6*(10+7)+9-8
104=6*(9+8)+7-5
105=6*(10+7)+8-5
106=6*(10+7)+9-5
107=6*(9+8)+10-5
108=6*(10+8)
109=6*(9+8)+7
110=6*(10+7)+8
111=6*(10+7)+9
112=6*(9+8)+10
113=6*(10+9)-8+7
114=6*(10+9)
115=6*(10+7)+5+8
116=6*(10+7)+5+9
117=6*(9+8)+5+10
118=10*(5+7)-8+6
119=10*(5+7)-9+8
120=10*(5+7)
121=10*(5+7)+9-8
122=10*(5+7)+8-6
123=10*(5+7)+9-6
124=7*(9+8)+5

Enjoy adding to this list!

TLW A Number To Find

N = 12

Solution: For each square

AA==BB
==EE==
CC==DD

the solution is given by

EE = ((CC * BB) – DD) / AA

[10degrees-admin]

@Sankaya, the result for NT3 for the first 1000 numbers is 250166416500.

[10degrees-admin]

The KA Answers – KA-6 (Ridiculous Questions)
1. Neither. If you and your partner had eleven clubs, the other two players would have two clubs.
2. The frog is deaf.
3. I can find four answers at least: One – Drop the thermometer from the top of the building and time how long it takes to reach the bottom (maybe when it smashes), before using the formula x=gt^2/2 (if you neglect air resistance, of course – the formula including air resistance is roughly x=(gt^2/2)-gt). Two – Measure the ratio of the thermometer’s height to the length of its shadow, then measure the length of the building’s shadow and use that to work out its height. Three – Find the superintendent and ask him to give you the height of the building in exchange for the thermometer. Four – Find the local DIY shop and ask the shopkeeper to exchange a tapemeasure (of quite a long length) for the thermometer, and then use the tapemeasure to measure the building’s height.

@Kford-academy Well done thank you for that, did you by chance use my program?

@Kford-academy,
125 = (5+8)*10-6
126 = (10+8)*7
127 = (10+9)*7-6
128 = (10+9)*7-5
129 = (6+7)*10-9+8
130 = (6+7)*10
131 = (10+9)*7-8+6
132 = (10+9)*7-6+5
133 = (10+9)*7
134 = (10+9)*7+6-5
135 = (10+9)*7+8-6
136 = (10+9)*7+8-5
138 = (5+6+9)*7-10+8
139 = (10+7)*8+9-6
140 = (6+8)*10
141 = (10+7)*8+5
142 = (9*8)-(7-6)*(10/5)
143 = 9*(6+10)-8+7
144 = 9*(6+10)
145 = 9*(6+10)-7+8
146 = (9*8)-(6-7)*(10/5)
147 = 10*(7+8)-9+6
148 = 10*(6+9)-7+5
149 = 10*(6+9)-8+7
150 = 10*(8+7)

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