Easy math puzzles
Poll
 | 20 votes (46.51%) | ||
| | 14 votes (32.55%) | ||
| | 6 votes (13.95%) | ||
| | 2 votes (4.65%) | ||
| | 12 votes (27.9%) | ||
| | 3 votes (6.97%) | ||
| | 6 votes (13.95%) | ||
| | 5 votes (11.62%) | ||
| | 12 votes (27.9%) | ||
| | 9 votes (20.93%) |
43 members have voted
March 4th, 2023 at 11:51:32 AM
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Quote: Ace2Estimates acceptable
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Estimates? The very idea!
The profit after 500 bets is:
73,757,475,375,627,846,307,350,078
436,536,886,123,015,558,692,237,218,084
692,158,059,537,793,457,579,981,781,280
182,993,521,187,538,472,164,180,680,104
217,264,621,453,665,842,270,932,365,204
942,756,160,837,394,641,602,376,922,656
629,794,518,893,012,361,700,069,097,416
708,674,157,480,315,734,489,616,273,805
841,861,659,192,166,453,194,723,121,455
402,733,639,736,117,928,058,574,923,471
985,905,474,167,372,420,726,357,160,161
714,830,811,049,311,991,163,790,306,775
217,342,204,513,295,346,053,543,267,155
091,722,965,213,587,322,592,091,184,261
888,503,257,423,955,271,125,909,335,321
085,870,653,981,415,068,197,230,888,165
194,549,612,640,658,289,777,497,642,374
530,061,655,801,041,398,886,370,606,794
078,624,886,187,002,018,927,625,285,361
252,209,596,541,827,484,009,843,207,339
376,072,806,708,086,053,131,731,384,222
419,601,413,874,419,308,397,355,071,283
711,920,733,625,187,423,386,013,113,845
397,688,991,700,058,688,933,903,173,922
957,188,360,650,204,798,031,091,450,228
517,324,439,397,176,579,838,520,595,787
348,987,299,858,068,169,644,388,697,047
798,520,683,822,967,546,322,989,483,881
578,884,410,987,254,394,717,299,161,910
568,910,618,715,338,590,480,118,154,645
973,621,103,368,869,246,254,710,034,831
349,743,888,352,326,236,336,073,655,374
472,227,348,791,547,146,536,842,860,495
433,652,597,587,169,315,756,780,910,907
731,574,923,761,737,606,578,220,402,431
121,446,885,304,781,886,395,603,759,804
433,288,175,819,835,762,580,462,804,643
982,068,455,329,633,522,755,627,202,911
420,301,976,650,964,536,429,078,444,685
337,566,843,945,290,394,622,153,941,570
979,710,497,050,636,449,149,466,379,610
505,427,600,358,589,952,417,606,956,897
505,093,547,354,024,938,297,228,697,200
377,334,691,775,391,981,743,970,269,332
382,613,429,384,835,428,021,547,149,800
/ 44,236,710,902,545,405,050,796
404,815,190,850,027,930,221,278,714,599
195,789,778,277,649,763,799,461,902,327
371,231,286,828,943,268,385,811,111,488
120,198,541,892,140,231,717,967,876,724
046,239,601,920,203,992,964,896,389,039
344,997,195,963,829,255,017,438,251,051
754,687,994,692,111,708,115,758,815,593
374,976,010,576,333,330,473,099,097,386
454,801,684,422,038,823,391,543,541,041
974,980,155,343,119,980,886,850,504,008
708,396,711,569,534,389,188,261,872,140
309,272,246,723,195,686,848,883,432,521
876,598,048,902,585,547,405,783,719,488
237,187,245,460,774,470,553,661,980,941
080,554,457,783,304,438,494,999,144,847
322,711,341,848,960,050,536,218,365,730
907,349,167,327,826,236,961,756,150,046
484,582,719,322,552,647,275,077,585,443
173,085,181,490,593,579,344,698,250,759
360,244,575,561,141,916,614,363,644,631
261,006,968,541,000,662,429,458,926,774
155,659,104,576,141,463,795,527,596,798
877,045,312,333,133,695,491,022,986,069
805,704,995,012,490,575,045,371,655,154
524,286,569,340,473,172,471,151,346,992
741,189,267,831,995,511,097,951,317,464
254,747,255,117,610,040,877,913,431,478
528,615,907,773,963,290,997,106,502,615
258,949,547,301,399,014,303,393,153,089
052,314,018,843,818,959,342,660,924,164
585,256,646,606,155,013,500,856,276,966
677,928,371,220,664,440,358,750,978,933
266,728,430,731,930,155,416,690,876,804
265,188,146,586,505,318,494,814,346,253
667,638,709,388,362,157,471,936,553,875
607,111,494,063,131,520,726,726,320,942
341,418,907,899,052,315,127,527,695,927
499,313,792,634,507,998,219,095,975,038
767,886,526,317,550,161,438,802,951,888
106,932,499,250,644,356,243,419,380,219
377,367,834,340,577,780,226,639,835,644
698,559,792,815,488,239,473,434,482,025
398,819,256,435,458,692,998,385,910,044
589,763,856,492,936,611,175,537,109,375
or about 1667.3363338
March 5th, 2023 at 12:26:22 PM
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I did also calculate, albeit with an approximation this time
The rebate needed for the house edge to be zero is about 14.8894165%
The rebate needed for the house edge to be zero is about 14.8894165%
March 5th, 2023 at 3:17:29 PM
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I’ll accept that answer. 16.7 unit gain. I assume you “Markoved” it for 500 iterations and backed out half the value of all the lossesQuote: ThatDonGuyQuote: Ace2Estimates acceptable
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Estimates? The very idea!
The profit after 500 bets is:
73,757,475,375,627,846,307,350,078
436,536,886,123,015,558,692,237,218,084
692,158,059,537,793,457,579,981,781,280
182,993,521,187,538,472,164,180,680,104
217,264,621,453,665,842,270,932,365,204
942,756,160,837,394,641,602,376,922,656
629,794,518,893,012,361,700,069,097,416
708,674,157,480,315,734,489,616,273,805
841,861,659,192,166,453,194,723,121,455
402,733,639,736,117,928,058,574,923,471
985,905,474,167,372,420,726,357,160,161
714,830,811,049,311,991,163,790,306,775
217,342,204,513,295,346,053,543,267,155
091,722,965,213,587,322,592,091,184,261
888,503,257,423,955,271,125,909,335,321
085,870,653,981,415,068,197,230,888,165
194,549,612,640,658,289,777,497,642,374
530,061,655,801,041,398,886,370,606,794
078,624,886,187,002,018,927,625,285,361
252,209,596,541,827,484,009,843,207,339
376,072,806,708,086,053,131,731,384,222
419,601,413,874,419,308,397,355,071,283
711,920,733,625,187,423,386,013,113,845
397,688,991,700,058,688,933,903,173,922
957,188,360,650,204,798,031,091,450,228
517,324,439,397,176,579,838,520,595,787
348,987,299,858,068,169,644,388,697,047
798,520,683,822,967,546,322,989,483,881
578,884,410,987,254,394,717,299,161,910
568,910,618,715,338,590,480,118,154,645
973,621,103,368,869,246,254,710,034,831
349,743,888,352,326,236,336,073,655,374
472,227,348,791,547,146,536,842,860,495
433,652,597,587,169,315,756,780,910,907
731,574,923,761,737,606,578,220,402,431
121,446,885,304,781,886,395,603,759,804
433,288,175,819,835,762,580,462,804,643
982,068,455,329,633,522,755,627,202,911
420,301,976,650,964,536,429,078,444,685
337,566,843,945,290,394,622,153,941,570
979,710,497,050,636,449,149,466,379,610
505,427,600,358,589,952,417,606,956,897
505,093,547,354,024,938,297,228,697,200
377,334,691,775,391,981,743,970,269,332
382,613,429,384,835,428,021,547,149,800
/ 44,236,710,902,545,405,050,796
404,815,190,850,027,930,221,278,714,599
195,789,778,277,649,763,799,461,902,327
371,231,286,828,943,268,385,811,111,488
120,198,541,892,140,231,717,967,876,724
046,239,601,920,203,992,964,896,389,039
344,997,195,963,829,255,017,438,251,051
754,687,994,692,111,708,115,758,815,593
374,976,010,576,333,330,473,099,097,386
454,801,684,422,038,823,391,543,541,041
974,980,155,343,119,980,886,850,504,008
708,396,711,569,534,389,188,261,872,140
309,272,246,723,195,686,848,883,432,521
876,598,048,902,585,547,405,783,719,488
237,187,245,460,774,470,553,661,980,941
080,554,457,783,304,438,494,999,144,847
322,711,341,848,960,050,536,218,365,730
907,349,167,327,826,236,961,756,150,046
484,582,719,322,552,647,275,077,585,443
173,085,181,490,593,579,344,698,250,759
360,244,575,561,141,916,614,363,644,631
261,006,968,541,000,662,429,458,926,774
155,659,104,576,141,463,795,527,596,798
877,045,312,333,133,695,491,022,986,069
805,704,995,012,490,575,045,371,655,154
524,286,569,340,473,172,471,151,346,992
741,189,267,831,995,511,097,951,317,464
254,747,255,117,610,040,877,913,431,478
528,615,907,773,963,290,997,106,502,615
258,949,547,301,399,014,303,393,153,089
052,314,018,843,818,959,342,660,924,164
585,256,646,606,155,013,500,856,276,966
677,928,371,220,664,440,358,750,978,933
266,728,430,731,930,155,416,690,876,804
265,188,146,586,505,318,494,814,346,253
667,638,709,388,362,157,471,936,553,875
607,111,494,063,131,520,726,726,320,942
341,418,907,899,052,315,127,527,695,927
499,313,792,634,507,998,219,095,975,038
767,886,526,317,550,161,438,802,951,888
106,932,499,250,644,356,243,419,380,219
377,367,834,340,577,780,226,639,835,644
698,559,792,815,488,239,473,434,482,025
398,819,256,435,458,692,998,385,910,044
589,763,856,492,936,611,175,537,109,375
or about 1667.3363338
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I used ((500^.5) * 4.92 * (2pi)^-.5 + 7.07) / 2 - 7.07 = 18.39 unit gain where 4.92 is the standard deviation and 7.07 the expected loss.
This number would be more accurate with more iterations
It’s all about making that GTA
March 5th, 2023 at 4:42:45 PM
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Quote: Ace2I assume you “Markoved” it for 500 iterations and backed out half the value of all the losses
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You assume correctly.
March 5th, 2023 at 4:54:26 PM
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To the first four significant digts I agree with both ThatDonGuy's figures based on a simple spreadsheet using its builtin function NORM.DIST .
1666.76, 0.14893
March 5th, 2023 at 5:07:06 PM
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I accept your answer as well.Quote: charliepatrickTo the first four significant digts I agree with both ThatDonGuy's figures
based on a simple spreadsheet using its builtin function NORM.DIST .1666.76, 0.14893
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It’s all about making that GTA
March 16th, 2023 at 6:58:30 AM
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This question was on the SAT exam many years ago. I am sure those of you that have studied math will get this easily but I chose what I thought was the obvious answer and was wrong.
Order from chaos
March 16th, 2023 at 7:51:42 AM
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In school, I learned that that the earth revolves around the sun whereas the earth rotates about the earth's axis.
Probably this SAT question should have worded the question as, "How many times will Circle A rotate in total?"
My answer is 4 rotations, but that is not one of the choices. Maybe, the questions should have included: (f) none of the above.
March 16th, 2023 at 8:04:23 AM
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Assume the small circle is like a tyre (tire) so sticks to the other circle as it rotates. At the start put a chalk mark at the base of the small circle (i.e. at 6 o'clock). Now push the tyre along the large circle.
The small circle's circumference is 1/3 pf the large circle so as it reaches 120 degrees (4 o'clock on the big circle) the chalk mark will be at the surface of the large circle. Thus the chalk mark will be at 10 o'clock. So at this stage the chalk mark/small circle has rotated 1 1/3 revolutions.
As this process continues, the other revolutions will also be 1 1/3, giving a total of 4 revolutions.
Another way of looking at this is when the small circle is a 3 o'clock, the chalk mark will be back at 6 o'clock, so rotated once.
The small circle's circumference is 1/3 pf the large circle so as it reaches 120 degrees (4 o'clock on the big circle) the chalk mark will be at the surface of the large circle. Thus the chalk mark will be at 10 o'clock. So at this stage the chalk mark/small circle has rotated 1 1/3 revolutions.
As this process continues, the other revolutions will also be 1 1/3, giving a total of 4 revolutions.
Another way of looking at this is when the small circle is a 3 o'clock, the chalk mark will be back at 6 o'clock, so rotated once.
March 18th, 2023 at 10:32:55 PM
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This was the math problem this week in my local alternative weekly:
seed
+iced
------
spice
1663
+9263
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10926
