Interesting Math Problems

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Re: Interesting Math Problems

#301

Post by Animal »

QillerDaemon wrote: ↑Sat Dec 17, 2022 9:40 pm 1 + 2 = 3
4 + 5 + 6 = 7 + 8
9 + 10 + 11 + 12 = 13 + 14 + 15
...

32 * 42 = 52
102 * 112 * 122 = 132 * 142
212 * 222 * 232 * 242 = 252 * 262 * 272
...

Questions:
1) What is the pattern that produces these series?
2) What is the next line or two of each series?
3) Does this hold for even higher exponents?
4) If not, how can it be made to hold true?
1. I have no idea what the name of the pattern is. The only pattern name that comes to mind is Fibonaci (sp?) numbers.
2. The next pattern on the top would be 16 + 17 + 18 + 19 + 20 = 21 + 22 + 23 + 24
I can't type out the pattern for the second one, but does it start with 36^2
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Re: Interesting Math Problems

#302

Post by Animal »

Also, you have a mistake in the way the problem is presented. In the 2nd series, they shouldn't be multiplied by each other, they should be added to each other. You have an asterisk between the numbers instead of plus signs.



32 * 42 = 52
102 * 112 * 122 = 132 * 142
212 * 222 * 232 * 242 = 252 * 262 * 272

That should read:

32 + 42 = 52
102 + 112 + 122 = 132 + 142
212 + 222 + 232 + 242 = 252 + 262 + 272

with the next one being:

36^2 + 37^2 + 38^2 + 39^2 + 40^2 = 41^2 + 42^2 + 43^2 + 44^2 = 7230

The the next in that series would start with 55^2 and equal to = 19,855
...
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Re: Interesting Math Problems

#303

Post by Animal »

3^3 + 4^3 + 5^3 = 6^3. which all equal 216

but i can't find another sequence going up from there that balances on both sides. I am sure there is one, I just haven't found it.
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Re: Interesting Math Problems

#304

Post by stonedmegman »

If it's 0F today and it'll be twice as cold tomorrow, how cold will it be?
I DON'T HAVE DUCKS IN A ROW. I HAVE SQUIRRELS AND THEY ARE AT A RAVE
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Re: Interesting Math Problems

#305

Post by Cyberhonky »

stonedmegman wrote: ↑Tue Jan 03, 2023 7:20 pm If it's 0F today and it'll be twice as cold tomorrow, how cold will it be?
-31.72F
Vote for Pedro
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Re: Interesting Math Problems

#306

Post by Antknot »

stonedmegman wrote: ↑Tue Jan 03, 2023 7:20 pm If it's 0F today and it'll be twice as cold tomorrow, how cold will it be?
Technically it’s not twice as cold it’s half as hot. So -459.63 / 2•-229.813F
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Re: Interesting Math Problems

#307

Post by Homebrew »

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Re: Interesting Math Problems

#308

Post by Animal »

:lol:
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Re: Interesting Math Problems

#309

Post by QillerDaemon »

A Diophantine equation:

2a + 2b + 2c = 2320

a = ?, b = ?, c = ?
a < b < c
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Re: Interesting Math Problems

#310

Post by Animal »

QillerDaemon wrote: ↑Mon Feb 06, 2023 3:12 pm A Diophantine equation:

2a + 2b + 2c = 2320

a = ?, b = ?, c = ?
a < b < c
a=4
b=8
c=11
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Re: Interesting Math Problems

#311

Post by Who »

Is this true?

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Re: Interesting Math Problems

#312

Post by Antknot »

Who wrote: ↑Mon Feb 06, 2023 10:54 pm Is this true?

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Re: Interesting Math Problems

#313

Post by Animal »

i can't count the number of times in my life i have said that exact same thing.
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Re: Interesting Math Problems

#314

Post by Bluespruce1964 »

Animal wrote: ↑Tue Feb 07, 2023 2:28 am i can't count the number of times in my life i have said that exact same thing.
At least trim it! 😀
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Re: Interesting Math Problems

#315

Post by QillerDaemon »

Animal wrote: ↑Mon Feb 06, 2023 8:08 pm
a=4
b=8
c=11
You didn't know show your work.know
If you can't be a good example, you can still serve as a horrible warning.
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Re: Interesting Math Problems

#316

Post by Animal »

QillerDaemon wrote: ↑Wed Feb 08, 2023 3:12 pm
Animal wrote: ↑Mon Feb 06, 2023 8:08 pm
a=4
b=8
c=11
You didn't know your work.
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10
3 4 5 6 7 8 9 10 11 12 4 5 6 7 8 9 10 11 12 13 5 6 7 8 9 10 11 12 13 14 6 7 8 9 10 11 12 13 14 15 7 8 9 10 11 12 13 14 15 16 8 9 10 11 12 13 14 15 16 17 9 10 11 12 13 14 15 16 17 18 10 11 12 13 14 15 16 17 18 19 11 12 13 14 15 16 17 18 19 20

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3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10
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3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
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YES
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448 704 1216 2240 4288 8384 16576 32960 65728 131264 832 1344 2368 4416 8512 16704 33088 65856 131392 262464 1600 2624 4672 8768 16960 33344 66112 131648 262720 524864 3136 5184 9280 17472 33856 66624 132160 263232 525376 1049664 6208 10304 18496 34880 67648 133184 264256 526400 1050688 2099264 12352 20544 36928 69696 135232 266304 528448 1052736 2101312 4198464 24640 41024 73792 139328 270400 532544 1056832 2105408 4202560 8396864 49216 81984 147520 278592 540736 1065024 2113600 4210752 8405056 16793664

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8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
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HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH

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Re: Interesting Math Problems

#317

Post by QillerDaemon »

What is that shit, Fortran IV?! :cartman:
If you can't be a good example, you can still serve as a horrible warning.
“All mushrooms are edible. Some even more than once!”
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Re: Interesting Math Problems

#318

Post by Animal »

QillerDaemon wrote: ↑Wed Feb 08, 2023 4:05 pm What is that shit, Fortran IV?! :cartman:
excel.
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Re: Interesting Math Problems

#319

Post by Homebrew »

Animal wrote: ↑Wed Feb 08, 2023 3:18 pm
QillerDaemon wrote: ↑Wed Feb 08, 2023 3:12 pm
Animal wrote: ↑Mon Feb 06, 2023 8:08 pm
a=4
b=8
c=11
You didn't know your work.
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10
3 4 5 6 7 8 9 10 11 12 4 5 6 7 8 9 10 11 12 13 5 6 7 8 9 10 11 12 13 14 6 7 8 9 10 11 12 13 14 15 7 8 9 10 11 12 13 14 15 16 8 9 10 11 12 13 14 15 16 17 9 10 11 12 13 14 15 16 17 18 10 11 12 13 14 15 16 17 18 19 11 12 13 14 15 16 17 18 19 20

14 22 38 70 134 262 518 1030 2054 4102 26 42 74 138 266 522 1034 2058 4106 8202 50 82 146 274 530 1042 2066 4114 8210 16402 98 162 290 546 1058 2082 4130 8226 16418 32802 194 322 578 1090 2114 4162 8258 16450 32834 65602 386 642 1154 2178 4226 8322 16514 32898 65666 131202 770 1282 2306 4354 8450 16642 33026 65794 131330 262402 1538 2562 4610 8706 16898 33282 66050 131586 262658 524802 3074 5122 9218 17410 33794 66562 132098 263170 525314 1049602

HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10
4 5 6 7 8 9 10 11 12 13 5 6 7 8 9 10 11 12 13 14 6 7 8 9 10 11 12 13 14 15 7 8 9 10 11 12 13 14 15 16 8 9 10 11 12 13 14 15 16 17 9 10 11 12 13 14 15 16 17 18 10 11 12 13 14 15 16 17 18 19 11 12 13 14 15 16 17 18 19 20

28 44 76 140 268 524 1036 2060 4108 8204 52 84 148 276 532 1044 2068 4116 8212 16404 100 164 292 548 1060 2084 4132 8228 16420 32804 196 324 580 1092 2116 4164 8260 16452 32836 65604 388 644 1156 2180 4228 8324 16516 32900 65668 131204 772 1284 2308 4356 8452 16644 33028 65796 131332 262404 1540 2564 4612 8708 16900 33284 66052 131588 262660 524804 3076 5124 9220 17412 33796 66564 132100 263172 525316 1049604

HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11
5 6 7 8 9 10 11 12 13 14 6 7 8 9 10 11 12 13 14 15 7 8 9 10 11 12 13 14 15 16 8 9 10 11 12 13 14 15 16 17 9 10 11 12 13 14 15 16 17 18 10 11 12 13 14 15 16 17 18 19 11 12 13 14 15 16 17 18 19 20 12 13 14 15 16 17 18 19 20 21

56 88 152 280 536 1048 2072 4120 8216 16408 104 168 296 552 1064 2088 4136 8232 16424 32808 200 328 584 1096 2120 4168 8264 16456 32840 65608 392 648 1160 2184 4232 8328 16520 32904 65672 131208 776 1288 2312 4360 8456 16648 33032 65800 131336 262408 1544 2568 4616 8712 16904 33288 66056 131592 262664 524808 3080 5128 9224 17416 33800 66568 132104 263176 525320 1049608 6152 10248 18440 34824 67592 133128 264200 526344 1050632 2099208

HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH

4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12
6 7 8 9 10 11 12 13 14 15 7 8 9 10 11 12 13 14 15 16 8 9 10 11 12 13 14 15 16 17 9 10 11 12 13 14 15 16 17 18 10 11 12 13 14 15 16 17 18 19 11 12 13 14 15 16 17 18 19 20 12 13 14 15 16 17 18 19 20 21 13 14 15 16 17 18 19 20 21 22

112 176 304 560 1072 2096 4144 8240 16432 32816 208 336 592 1104 2128 4176 8272 16464 32848 65616 400 656 1168 2192 4240 8336 16528 32912 65680 131216 784 1296 2320 4368 8464 16656 33040 65808 131344 262416 1552 2576 4624 8720 16912 33296 66064 131600 262672 524816 3088 5136 9232 17424 33808 66576 132112 263184 525328 1049616 6160 10256 18448 34832 67600 133136 264208 526352 1050640 2099216 12304 20496 36880 69648 135184 266256 528400 1052688 2101264 4198416
YES
HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH

5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13
7 8 9 10 11 12 13 14 15 16 8 9 10 11 12 13 14 15 16 17 9 10 11 12 13 14 15 16 17 18 10 11 12 13 14 15 16 17 18 19 11 12 13 14 15 16 17 18 19 20 12 13 14 15 16 17 18 19 20 21 13 14 15 16 17 18 19 20 21 22 14 15 16 17 18 19 20 21 22 23

224 352 608 1120 2144 4192 8288 16480 32864 65632 416 672 1184 2208 4256 8352 16544 32928 65696 131232 800 1312 2336 4384 8480 16672 33056 65824 131360 262432 1568 2592 4640 8736 16928 33312 66080 131616 262688 524832 3104 5152 9248 17440 33824 66592 132128 263200 525344 1049632 6176 10272 18464 34848 67616 133152 264224 526368 1050656 2099232 12320 20512 36896 69664 135200 266272 528416 1052704 2101280 4198432 24608 40992 73760 139296 270368 532512 1056800 2105376 4202528 8396832

HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH

6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14
8 9 10 11 12 13 14 15 16 17 9 10 11 12 13 14 15 16 17 18 10 11 12 13 14 15 16 17 18 19 11 12 13 14 15 16 17 18 19 20 12 13 14 15 16 17 18 19 20 21 13 14 15 16 17 18 19 20 21 22 14 15 16 17 18 19 20 21 22 23 15 16 17 18 19 20 21 22 23 24

448 704 1216 2240 4288 8384 16576 32960 65728 131264 832 1344 2368 4416 8512 16704 33088 65856 131392 262464 1600 2624 4672 8768 16960 33344 66112 131648 262720 524864 3136 5184 9280 17472 33856 66624 132160 263232 525376 1049664 6208 10304 18496 34880 67648 133184 264256 526400 1050688 2099264 12352 20544 36928 69696 135232 266304 528448 1052736 2101312 4198464 24640 41024 73792 139328 270400 532544 1056832 2105408 4202560 8396864 49216 81984 147520 278592 540736 1065024 2113600 4210752 8405056 16793664

HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH

7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 15 15 15 15 15 15 15 15 15 15
9 10 11 12 13 14 15 16 17 18 10 11 12 13 14 15 16 17 18 19 11 12 13 14 15 16 17 18 19 20 12 13 14 15 16 17 18 19 20 21 13 14 15 16 17 18 19 20 21 22 14 15 16 17 18 19 20 21 22 23 15 16 17 18 19 20 21 22 23 24 16 17 18 19 20 21 22 23 24 25

896 1408 2432 4480 8576 16768 33152 65920 131456 262528 1664 2688 4736 8832 17024 33408 66176 131712 262784 524928 3200 5248 9344 17536 33920 66688 132224 263296 525440 1049728 6272 10368 18560 34944 67712 133248 264320 526464 1050752 2099328 12416 20608 36992 69760 135296 266368 528512 1052800 2101376 4198528 24704 41088 73856 139392 270464 532608 1056896 2105472 4202624 8396928 49280 82048 147584 278656 540800 1065088 2113664 4210816 8405120 16793728 98432 163968 295040 557184 1081472 2130048 4227200 8421504 16810112 33587328

HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH

8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 15 15 15 15 15 15 15 15 15 15 16 16 16 16 16 16 16 16 16 16
10 11 12 13 14 15 16 17 18 19 11 12 13 14 15 16 17 18 19 20 12 13 14 15 16 17 18 19 20 21 13 14 15 16 17 18 19 20 21 22 14 15 16 17 18 19 20 21 22 23 15 16 17 18 19 20 21 22 23 24 16 17 18 19 20 21 22 23 24 25 17 18 19 20 21 22 23 24 25 26

1792 2816 4864 8960 17152 33536 66304 131840 262912 525056 3328 5376 9472 17664 34048 66816 132352 263424 525568 1049856 6400 10496 18688 35072 67840 133376 264448 526592 1050880 2099456 12544 20736 37120 69888 135424 266496 528640 1052928 2101504 4198656 24832 41216 73984 139520 270592 532736 1057024 2105600 4202752 8397056 49408 82176 147712 278784 540928 1065216 2113792 4210944 8405248 16793856 98560 164096 295168 557312 1081600 2130176 4227328 8421632 16810240 33587456 196864 327936 590080 1114368 2162944 4260096 8454400 16843008 33620224 67174656

HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH HIGH

9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 15 15 15 15 15 15 15 15 15 15 16 16 16 16 16 16 16 16 16 16 17 17 17 17 17 17 17 17 17 17
11 12 13 14 15 16 17 18 19 20 12 13 14 15 16 17 18 19 20 21 13 14 15 16 17 18 19 20 21 22 14 15 16 17 18 19 20 21 22 23 15 16 17 18 19 20 21 22 23 24 16 17 18 19 20 21 22 23 24 25 17 18 19 20 21 22 23 24 25 26 18 19 20 21 22 23 24 25 26 27

3584 5632 9728 17920 34304 67072 132608 263680 525824 1050112 6656 10752 18944 35328 68096 133632 264704 526848 1051136 2099712 12800 20992 37376 70144 135680 266752 528896 1053184 2101760 4198912 25088 41472 74240 139776 270848 532992 1057280 2105856 4203008 8397312 49664 82432 147968 279040 541184 1065472 2114048 4211200 8405504 16794112 98816 164352 295424 557568 1081856 2130432 4227584 8421888 16810496 33587712 197120 328192 590336 1114624 2163200 4260352 8454656 16843264 33620480 67174912 393728 655872 1180160 2228736 4325888 8520192 16908800 33686016 67240448 134349312

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QillerDaemon
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Re: Interesting Math Problems

#320

Post by QillerDaemon »

If you can't be a good example, you can still serve as a horrible warning.
“All mushrooms are edible. Some even more than once!”
これを グーグル 翻訳に登録してくれておめでとう、バカ。
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stonedmegman
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Re: Interesting Math Problems

#321

Post by stonedmegman »

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I DON'T HAVE DUCKS IN A ROW. I HAVE SQUIRRELS AND THEY ARE AT A RAVE
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QillerDaemon
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Re: Interesting Math Problems

#322

Post by QillerDaemon »

There is a right triangle, and inside it is drawn a circle that is tangent to all three sides. The shortest leg of the triangle is 32 units, and radius of the circle is 12 units. What is the area of the triangle? Hint: two tangent theorem
If you can't be a good example, you can still serve as a horrible warning.
“All mushrooms are edible. Some even more than once!”
これを グーグル 翻訳に登録してくれておめでとう、バカ。
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Animal
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Re: Interesting Math Problems

#323

Post by Animal »

i can't show my work (and didn't look at the hint, so i'm not sure if that changes how you want the answer), but I get the area of the triangle as about 216.4615.
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QillerDaemon
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Re: Interesting Math Problems

#324

Post by QillerDaemon »

Good try, but unfortunately wrong. The answer is an integer with three places, and over three times as big as your answer. While there are other ways to solve the problem, the two tangent theorem makes it easy. Problems like this, unless they involve solutions on circular diagrams, are almost always integer answers, and even if circular, almost involve integer multiples of pi or easy fractions of pi.

The two tangent theorem states that two line segments tangent to the same circle that meet at a point outside the circle have the same length from the tangent point to the outside point, ie congruent. That helps you set up formulas for the lengths of the unknown sides of the triangle. Pythagorean theorem and Bob's your uncle.
If you can't be a good example, you can still serve as a horrible warning.
“All mushrooms are edible. Some even more than once!”
これを グーグル 翻訳に登録してくれておめでとう、バカ。
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CentralTexasCrude
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Re: Interesting Math Problems

#325

Post by CentralTexasCrude »

I was told there would be no tests on Sunday
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