Megapizza

Megapizza will be divided among 100 people. First gets 1%, 2nd 2% of the remainder, 3rd 3% of the remainder, etc. Last 100th 100% of the remainder. Which person got the biggest portion?

Correct answer:

n =  10

Step-by-step explanation:

r1​=1001​⋅ 1=0.01 r2​=1002​⋅ 0.99=500099​=0.0198 r3​=1003​⋅ 0.9702≐0.0291 r4​=1004​⋅ 0.941094≐0.0376 r5​=1005​⋅ 0.90345024≐0.0452 r6​=1006​⋅ 0.858277728≐0.0515 r7​=1007​⋅ 0.80678106432≐0.0565 r8​=1008​⋅ 0.7503063898176≐0.06 r9​=1009​⋅ 0.69028187863219≐0.0621 r10​=10010​⋅ 0.62815650955529≐0.0628 r11​=10011​⋅ 0.56534085859977≐0.0622 r12​=10012​⋅ 0.50315336415379≐0.0604 r13​=10013​⋅ 0.44277496045534≐0.0576 r14​=10014​⋅ 0.38521421559614≐0.0539 r15​=10015​⋅ 0.33128422541268≐0.0497 r16​=10016​⋅ 0.28159159160078≐0.0451 r17​=10017​⋅ 0.23653693694466≐0.0402 r18​=10018​⋅ 0.19632565766406≐0.0353 r19​=10019​⋅ 0.16098703928453≐0.0306 r20​=10020​⋅ 0.13039950182047≐0.0261 r21​=10021​⋅ 0.10431960145638≐0.0219 r22​=10022​⋅ 0.082412485150538≐0.0181 r23​=10023​⋅ 0.06428173841742≐0.0148 r24​=10024​⋅ 0.049496938581413≐0.0119 r25​=10025​⋅ 0.037617673321874≐0.0094 r26​=10026​⋅ 0.028213254991405≐0.0073 r27​=10027​⋅ 0.02087780869364≐0.0056 r28​=10028​⋅ 0.015240800346357≐0.0043 r29​=10029​⋅ 0.010973376249377≐0.0032 r30​=10030​⋅ 0.0077910971370578≐0.0023 r31​=10031​⋅ 0.0054537679959405≐0.0017 r32​=10032​⋅ 0.0037630999171989≐0.0012 r33​=10033​⋅ 0.0025589079436953≐0.0008 r34​=10034​⋅ 0.0017144683222758≐0.0006 r35​=10035​⋅ 0.001131549092702≐0.0004 r36​=10036​⋅ 0.00073550691025633≐0.0003 r37​=10037​⋅ 0.00047072442256405≐0.0002 r38​=10038​⋅ 0.00029655638621535≐0.0001 r39​=10039​⋅ 0.00018386495945352≐0.0001 r40​=10040​⋅ 0.00011215762526665≐4.4863⋅10−5 r41​=10041​⋅ 6.7294575159988⋅10−5≐2.7591⋅10−5 r42​=10042​⋅ 3.9703799344393⋅10−5≐1.6676⋅10−5 r43​=10043​⋅ 2.3028203619748⋅10−5≐9.9021⋅10−6 r44​=10044​⋅ 1.3126076063256⋅10−5≐5.7755⋅10−6 r45​=10045​⋅ 7.3506025954235⋅10−6≐3.3078⋅10−6 r46​=10046​⋅ 4.0428314274829⋅10−6≐1.8597⋅10−6 r47​=10047​⋅ 2.1831289708408⋅10−6≐1.0261⋅10−6 r48​=10048​⋅ 1.1570583545456⋅10−6≐5.5539⋅10−7 r49​=10049​⋅ 6.0167034436372⋅10−7≐2.9482⋅10−7 r50​=10050​⋅ 3.068518756255⋅10−7≐1.5343⋅10−7 r51​=10051​⋅ 1.5342593781275⋅10−7≐7.8247⋅10−8 r52​=10052​⋅ 7.5178709528247⋅10−8≐3.9093⋅10−8 r53​=10053​⋅ 3.6085780573558⋅10−8≐1.9125⋅10−8 r54​=10054​⋅ 1.6960316869572⋅10−8≐9.1586⋅10−9 r55​=10055​⋅ 7.8017457600033⋅10−9≐4.291⋅10−9 r56​=10056​⋅ 3.5107855920015⋅10−9≐1.966⋅10−9 r57​=10057​⋅ 1.5447456604807⋅10−9≐8.8051⋅10−10 r58​=10058​⋅ 6.6424063400668⋅10−10≐3.8526⋅10−10 r59​=10059​⋅ 2.7898106628281⋅10−10≐1.646⋅10−10 r60​=10060​⋅ 1.1438223717595⋅10−10≐6.8629⋅10−11 r61​=10061​⋅ 4.575289487038⋅10−11≐2.7909⋅10−11 r62​=10062​⋅ 1.7843628999448⋅10−11≐1.1063⋅10−11 r63​=10063​⋅ 6.7805790197904⋅10−12≐4.2718⋅10−12 r64​=10064​⋅ 2.5088142373224⋅10−12≐1.6056⋅10−12 r65​=10065​⋅ 9.0317312543608⋅10−13≐5.8706⋅10−13 r66​=10066​⋅ 3.1611059390263⋅10−13≐2.0863⋅10−13 r67​=10067​⋅ 1.0747760192689⋅10−13≐7.201⋅10−14 r68​=10068​⋅ 3.5467608635875⋅10−14≐2.4118⋅10−14 r69​=10069​⋅ 1.134963476348⋅10−14≐7.8312⋅10−15 r70​=10070​⋅ 3.5183867766788⋅10−15≐2.4629⋅10−15 r71​=10071​⋅ 1.0555160330036⋅10−15≐7.4942⋅10−16 r72​=10072​⋅ 3.0609964957105⋅10−16≐2.2039⋅10−16 r73​=10073​⋅ 8.5707901879895⋅10−17≐6.2567⋅10−17 r74​=10074​⋅ 2.3141133507572⋅10−17≐1.7124⋅10−17 r75​=10075​⋅ 6.0166947119686⋅10−18≐4.5125⋅10−18 r76​=10076​⋅ 1.5041736779922⋅10−18≐1.1432⋅10−18 r77​=10077​⋅ 3.6100168271812⋅10−19≐2.7797⋅10−19 r78​=10078​⋅ 8.3030387025167⋅10−20≐6.4764⋅10−20 r79​=10079​⋅ 1.8266685145537⋅10−20≐1.4431⋅10−20 r80​=10080​⋅ 3.8360038805627⋅10−21≐3.0688⋅10−21 r81​=10081​⋅ 7.6720077611254⋅10−22≐6.2143⋅10−22 r82​=10082​⋅ 1.4576814746138⋅10−22≐1.1953⋅10−22 r83​=10083​⋅ 2.6238266543049⋅10−23≐2.1778⋅10−23 r84​=10084​⋅ 4.4605053123183⋅10−24≐3.7468⋅10−24 r85​=10085​⋅ 7.1368084997093⋅10−25≐6.0663⋅10−25 r86​=10086​⋅ 1.0705212749564⋅10−25≐9.2065⋅10−26 r87​=10087​⋅ 1.498729784939⋅10−26≐1.3039⋅10−26 r88​=10088​⋅ 1.9483487204206⋅10−27≐1.7145⋅10−27 r89​=10089​⋅ 2.3380184645048⋅10−28≐2.0808⋅10−28 r90​=10090​⋅ 2.5718203109553⋅10−29≐2.3146⋅10−29 r91​=10091​⋅ 2.5718203109553⋅10−30≐2.3404⋅10−30 r92​=10092​⋅ 2.3146382798597⋅10−31≐2.1295⋅10−31 r93​=10093​⋅ 1.8517106238878⋅10−32≐1.7221⋅10−32 r94​=10094​⋅ 1.2961974367214⋅10−33≐1.2184⋅10−33 r95​=10095​⋅ 7.7771846203287⋅10−35≐7.3883⋅10−35 r96​=10096​⋅ 3.8885923101643⋅10−36≐3.733⋅10−36 r97​=10097​⋅ 1.5554369240657⋅10−37≐1.5088⋅10−37 r98​=10098​⋅ 4.6663107721972⋅10−39≐4.573⋅10−39 r99​=10099​⋅ 9.3326215443944⋅10−41≐9.2393⋅10−41 r100​=100100​⋅ 9.3326215443945⋅10−43≐9.3326⋅10−43 r10​>∀r r10​…max n=10

Try another example


Did you find an error or inaccuracy? Feel free to write us. Thank you!



Showing 1 comment:
#
Dr Math
Perhaps a more elegant solution: The Kth person gets 99! / (99 - (k-1)! * K / 100exp (k). K + 1. The person gets 99! / (99 - k)! * (K + 1) / 100exp (k + 1) The ratio m (k + 1) / m (k) must be greater than one, ie: the next person in the order will receive a larger portion than the previous one.Applies to k = 1, 2, … 9. The 10th person gets the largest portion.

avatar







Tips to related online calculators
Need help to calculate sum, simplify or multiply fractions? Try our fraction calculator.
Our percentage calculator will help you quickly calculate various typical tasks with percentages.

You need to know the following knowledge to solve this word math problem:


 
We encourage you to watch this tutorial video on this math problem: video1

Related math problems and questions: