Ciphers and Puzzles from Competitors

===================================== ANSWER
TLW A Number To Find
=====================
ANSWER 12

09==06
==06==
11==12

If we letter the square thus:
A=B
=E=
D=C

Then the 4 corner numbers relationship to the center square number is:
((D*B)-C)/A = E
so
((11*6)-C)/9 = 6
rearrange
(D*B)-(A*E) = C
(11*6)-(9*6) = 12

So @Puttputt86 is correct – well done for that one.

[10degrees-admin]

@Prabhaa, (5+8)*10-6 equals 124. Try again!

TLW MISSING NUMBERS
===================
Eleven for elevenses (rating *).

To keep the grids the same size I have used leading zeros.
The x’s are where the missing number needs to go – they are only place
holders, they do not represent how many digits a number has.

A little logic and a little math is all you need.

Only post when you have ALL 11 answers – I wonder who that will be?

============================ #1
[628][401][xxx][231]
[862][140][990][123]
============================ #2
[07][03][11]
[09][05][22]
[xx][02][27]
============================ #3
[14][63][42]
[02][09][06]
[35][xx][70]
[05][04][10]
============================ #4
[21][17][53][40]
[16][66][xx][28]
[45][59][77][82]
[93][44][89][103]
============================ #5
[019][038][057][076]
[034][068][xxx][136]
[073][146][219][292]
============================ #6
[14][11][08][05]
[xx][19][14][09]
============================ #7
[16][06][39][03]
[24][02][36][xx]
[11][01][48][02]
============================ #8
[101][47][55][01]
[063][88][11][36]
[034][17][17][00]
[025][xx][48][32]
============================ #9
____[124]
__[x]___[3]
__[16]_[4]
_____[7]
============================ #10
______[4]
_____[xxx]
____[_324_]
___[__2916_]
__[__26244__]
_[___236196__]
============================ #11
[00003][00003][00006][00018]
[00072][xxxxx][02160][15120]
============================

KA-6 #3

Five. Stop numerous passers-by. Ask each of them how tall they are (feet to shoulders) and ask them to stand on each other’s shoulders until they are as tall as the building. Give them the thermometer as a show of your appreciation for their time, energy and risk…

@Kford-academy,
125 = 5*(10+9+6)
151 = 5*(10*(9-6))+(8-7)
152 = 9*(10+7)-(6-5)
153 = 9*(10+7)
154 = 9*(10+7)+(6-5)
155 = 5*(10*(9-6)+(8-7))
156 = (5+7)*(10+9-6)
157 = 9*(10+8)-5
158 = 9*(10+7)+5
159 = 9*(10+7)+6
160 = 9*(10+8)-(7-5)

[10degrees-admin]

Sorry, did I say one of the formulas was x=(gt^2/2)-gt? I meant x=(gt^2/2)-(Dgt)^2, where D is the diameter of the thermometer if it was a sphere!

[10degrees-admin]

The KA Answers – KA-8 (The Countdown Conundrum) – Part 1
And yes, you can make every number from 100 to 999! First set of 50 here.
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
125=7*(9+8)+6
126=7*(10+8)
127=7*(10+8)+6-5
128=8*(9+7)
129=8*(10+5)+9
130=8*(9+6)+10
131=8*(9+7)+6*5/10
132=8*(9+7)+10-6
133=8*(9+7)+5
134=8*(9+7)+6
135=8*(10+6)+7
136=8*(10+7)
137=8*(10+6)+9
138=8*(9+7)+10
139=10*(5+9)-7+6
140=10*(5+9)
141=10*(5+9)+7-6
142=10*(5+9)+8-6
143=10*(6+9)-7
144=10*(7+8)-6
145=10*(7+8)-5
146=10*(7+8)-9+5
147=10*(7+8)-9+6
148=10*(6+9)-7+5
149=10*(7+8)-6+5

[10degrees-admin]

The KA Answers – KA-7 (The Second Riddle of the Sphinx)
The answer: night and day. Well done to @Madness for being the only one to get this correct!

[10degrees-admin]

Just a note about my last post: the diameter must be less than about 50cm for the formula to work, and even then it might not work for the whole length – if the diameter was 10cm, the formula would be invalid after about 5m!

[10degrees-admin]

I don’t have time to proofread my answers, and I found a few mistakes in the answers to KA-6, so I thought that I’d do an updated version!
—
The KA Answers – KA-6 (Ridiculous Questions) – Updated Version!
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)-((Dgt)^2/5) (see bottom for notes on this formula)). 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.

Notes:
1. Thanks to @Puttputt86 for another answer for number 3: “Stop numerous passers-by. Ask each of them how tall they are (feet to shoulders) and ask them to stand on each other’s shoulders until they are as tall as the building. Give them the thermometer as a show of your appreciation for their time, energy and risk…”
2. For the formula ‘x=(gt^2/2)-((Dgt)^2/5)’, D refers to the effective diameter of the thermometer.
3. Also for the formula ‘x=(gt^2/2)-((Dgt)^2/5)’, there are a few limitations. Two being that D must be less than 0.5m, and even then it might not work for the entire length of the building. For example, if D was 0.2m, the formula would go out of tolerance after roughly 1.2 seconds, or a drop of roughly 7.5m!

KA-6 (Ridiculous Questions) Number 3 Ha, ha non worked for me…

Four: Shop keeper – “Get out of here! If you want a tape measure, buy one, this is not a swap-shop!”
Three: Superintendent – “What makes you think I know the height and what do you want to know for? Go away before I call the police!”
Two: Because of the suns position relative the buildings position it never casts a shadow to the ground but onto surrounding buildings.
One: I do not have an accurate stop watch, I’m deaf, I do not like heights, so that is a no no!

By the way did you hear about the miser who dropped a penny from his 5th story flat?
It hit him on his head!

TLW NUMBER THEORY CONTINUED (all rated *)(I would like to see your script/workings)
===========================
================================================================ NT4
The four adjacent digits in the given 1000-digit number
that have the greatest product are 9 × 9 × 8 × 9 = 5832.

7316717653133062491922511967442657474235534919493496983520312774506326
2395783180169848018694788518438586156078911294949545950173795833195285
3208805511125406987471585238630507156932909632952274430435576689664895
0445244523161731856403098711121722383113622298934233803081353362766142
8280644448664523874930358907296290491560440772390713810515859307960866
7017242712188399879790879227492190169972088809377665727333001053367881
2202354218097512545405947522435258490771167055601360483958644670632441
5722155397536978179778461740649551492908625693219784686224828397224137
5657056057490261407972968652414535100474821663704844031998900088952434
5065854122758866688116427171479924442928230863465674813919123162824586
1786645835912456652947654568284891288314260769004224219022671055626321
1111093705442175069416589604080719840385096245544436298123098787992724
4284909188845801561660979191338754992005240636899125607176060588611646
7109405077541002256983155200055935729725716362695618826704282524836008
23257530420752963450

Find the thirteen adjacent digits in the 1000-digit number that have
the greatest product.
What is the value of this product?

Note: The number has been split to 70 digits per line, you will need
to join the lines to work on the full number.

================================================================ NT5
TLW Largest product in a grid
=============================
In the 20×20 grid below, four numbers along a diagonal line have been marked.

08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
32 98 81 28 64 23 67 10[26]38 40 67 59 54 70 66 18 38 64 70
67 26 20 68 02 62 12 20 95[63]94 39 63 08 40 91 66 49 94 21
24 55 58 05 66 73 99 26 97 17[78]78 96 83 14 88 34 89 63 72
21 36 23 09 75 00 76 44 20 45 35[14]00 61 33 97 34 31 33 95
78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48

The product of these numbers is 26 × 63 × 78 × 14 = 1788696.

What is the greatest product of four adjacent numbers in a strait line of the same direction (up, down, left, right, or diagonally) in the 20×20 grid?

Give answer of the 4 numbers and their product: n*n*n*n = p

================================================================ NT6
Self powers
===========
The series, 1^1 + 2^2 + 3^3 + … + 10^10 = 10405071317.

Find the last ten digits of the series, 1^1 + 2^2 + 3^3 + … + 1000^1000.

================================================================ NT7
Powerful digit sum
==================
A googol (10^100) is a massive number: one followed by one-hundred zeros;
100^100 is almost unimaginably large: one followed by two-hundred zeros.
Despite their size, the sum of the digits in each number is only 1.

Considering natural numbers of the form, a^b, where a, b < 100,
what is the maximum digital sum?

================================================================ NT8
Large non-Mersenne prime
========================
The first known prime found to exceed one million digits was discovered in 1999, and is a Mersenne prime of the form 2^6972593−1; it contains exactly 2,098,960 digits. Subsequently other Mersenne primes, of the form 2^p−1, have been found which contain more digits.

However, in 2004 there was found a massive non-Mersenne prime which contains 2,357,207 digits: 28433×2^7830457+1.

Find the last ten digits of this prime number.

================================================================

[10degrees-admin]

NT5 – 87*97*94*89=70600674?

[10degrees-admin]

KA-9

If:
1879*3=legs,
122*41=zoos,
20*18000+1780=oblige,
70038+2^4*3*5^2=bezil,
and (2*7+30*40+12000-20*100)/2=logs,
then what does 2*(2500+3*51) equal?

NT4 23514624000?
NT5 70600674?
NT6 1297461358?

[Author]

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