IMO Math Olympiad Preparation : Useful trip and tricks

Ektg Hdyep`km Mh‐s klm Mhl‐ts

[uist`hls & Nhlnirls • Lht suri ghw th pripkri bhr Hdyep`km. • Ey mkujgtir prknt`nim kdd quist`hls brhe tixtahhf. ^t`dd m`m lht mh widd `l Hdyep`km. • @EH bhddhws skei nurr`nudue, st`dd Hdyep`km quist`hls dhhfs sh m`bbirilt.

Hdyep`km ? Zgkt `s m`bbirilt8 • E`x`lj hb sf`dds • G`jgir jrkmi quist`hls • [uist`hls `ltilt`hlkddy nriktim th nhlbusi

E`x`lj hb sf`dds ]kp K, wg`ng gks k n`rnudkr hpil`lj hb ; ne rkm`us, b`dds k tklf `l =3 e`luti. ]giri `s klhtgir tkp wg`ng gks kl n`rnudkr hpil`lj hb 1 ne rkm`us. @b ahtg tkps kri hpilim thjitgir b`lm tgi t`ei tkfil th b`dd tgi tklf.

• Gkrm bhr k e`mmdi jrkmi stumilt hasirvi vi nkribud nkribuddy dy `t gks bhddhw` bhddhw`lj lj pkrts pkrts • @b yhu hasir  „ B`lm tgi t`ei tkfil ay sinhlm tkp th b`dd b `dd tgi tklf • Qiqu`rim sf`dd ? Krik hb n`rndi, nhlnipt hb prhphrt`hls

 „ J`vil tgi twh t`eis, b`lm thtkd t`ei wgil ahtg kri hpil • Qiqu`rim sf`dd ? @lvirsi prhphrt`hls

G`jgir jrkmi quist`hls B`lm tgi krik

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]g`s eky ai ksfim `l k jrkmi wgiri  „ Phu kri tkujgt hldy hldy tgi krik hb hb rintkljdis  „  Krik hb sung nhepdix nhepdix sgkpis `s lht lht nhvirim

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Aut `b yhu tg`lf (hr gkvi gkvi siil sung quist`h quist`hls ls mur`lj mur`lj prknt`n prknt`ni) i)  „  Kri hb sgkpi 5 Krik hb rintkljdi + Krik hb tr`kljdi  „  Krik hb tr`kljdi tr`kljdi 5 µ Krik hb rintkljdi

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Ivil `b tgi sf`dd usim `l tgi quist`hl dhhfs ulflhwl  „ Nkl st`dd shdvi `t us`lj k —flhwl sf`dd + nheehl nheehl silsi―

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Hb-nhursi `t `s iks`ir sk`m tgkl mhli.  „ @t `s `ephrtklt th prknt`ni ks ekly ekly quist`hls ks yhu yhu nkl.

Nhlbus`lj quist`hls ^udifgk gks 7 pk`r hb rim shnfs shnfs klm 7 pk`r hb purpdi shnfs. shnfs. Kdd tgi shnfs kri kri `l k akj, `b ^udifgk p`nfs tgi shnfs shnfs w`tghut w`tghut dhhf`lj kt tgie, ghw ekly shnfs sgi gks th riehvi brhe tgi akj aibhri sgi nkl ai suri tgkt sgi gks k pk`r hb k s`ljdi nhdhr 8

• F`ms gkvi k tilmilny th tg`lf,  „ ]h b`lm klswir, kdd tgi lueairs j`vil `l quist`hl liim th ai usim sheigh sheighw w (@t eky shulm shulm hmm aut stum`is stum`is sghw tgkt tgkt tg`s `s trui).

• ]gi klswir `s tgrii,  „ @l tgrii shnfs yhu kri jukrkltiim th gkvi twh shnfs s hnfs hb skei nhdhr   „ Ekl Ekly y f`ms f`ms kls klswir wir ks ;:

• Sh`lt giri `s th riek`l bhnusim hl tgi quist`hl klm lht th ji jitt nhlb nhlbusi usim. m.

^trunturim Dikrl`lj • Ylmirstklm tgi m`bbirilni aitwiil thp`n klm sf`dds  „ Ixkepdi sf`dds bhr [ukmrkt`n iqukt`hls • shdvi qukmrkt`n iqukt`hls us`lj bknthr`zkt`hl • nhlm`t`hls bhr ul`qui/rikd shdut`hl th ix`st • Qiprisilt`lj rikd d`bi prhadies us`lj [ukmrkt`n iqukt`hl •  Kppd`nkt  Kppd`nkt`hl `hl `l whrm prhadies

Qijudkr Ixke Nhlnipts Kdjiark

Srhaka`d`ty

Brknt`hls

]r`jhlheitry

Qijudkr ixke (kppd`nkt`hl hb nhlnipts)

Kdjiark Brknt`hls

]r`jhlheitry Srhaka`d`ty Jiheitry

~933 typi hb quist`hls pir jrkmi

Jiheitry

Hdyep`km Hdyep`km

Brknt`hls Jiheitry Brknt`hls

]r`jhlheitry Kdjiark

Srhaka`d`ty ]r`jhlheitry

Kdjiark Kdjiark

Brknt`hls 8

Brknt`hls+ Jiheitry+

Kdjiark

Kdjiark

Jiheitry

•  Kppd`nkt`hl hb e`xim nhlnipts • Ixtilmim nhlnipts (ix`st`lj + nheehl-silsi) • Nhlbus`lj idieilts

<93,333 typi hb quist`hls qui st`hls pir jrkmi

Zgkt th mh ? Aibhri Ixke • @milt`by kdd tgi sf`dds hb k thp`n  „ Ekfi suri th ulmirstklm kdd hb tgie.

• Ylmirstklm tgi nhlnipt hb sf`dds  „ Ysi tgihry brhe LNIQ] ahhfs  „ @b mhuat, nhlsudt w`tg yhur tikngir hr yhu nkl kdsh ksf ixpir ix pirts ts `l shei shei hld` hld`li li bhrue bhrue (i.j. (i.j. Imu Imujk` jk`l l [& [&K). K).

• Srknt`ni ks eung ks yhu nkl.  „ Qijudkr ahhfs eky lht prhv`mi vkr`ity hb quist`hls.  „ Nhls`mir us`lj hld`li rishurnis (i.j. www.imujk`l.nhe)) th prknt`ni uld`e`tim www.imujk`l.nhe uld`e`tim vkr`ity hb quist`hls.

Zgkt th mh ? Mur`lj Ixke k m t g i n h e p d i t i q u i s t ` h l n k r i b u d d y .  • Mh lht pkl`n klm r i km  „ @ephrtklt bhr ixke d`fi Hdyep`km wgiri quist`hls kri nhlbus`lj shei ixtrk sinhlms sinhlms th ulmirstkl ulmirstklm m tgi quist`hl quist`hl  „ @t `s hf th spilm shei • Qktgir tgkl mh`lj `t `lnhrrintdy klm kjk`l spilm`lj ixtrk t`ei, wgil yhur klswir mhis lht ektngis kly hb tgi j`vil ngh`nis.

• @b quist`hl dhhfs thujg, try th arikf tgi prhadie `lth pkrts. • Ghwivir gkrm tgi quist`hl e`jgt dhhf, `t `s kdehst suri tgkt kdd tgi sf`dds usim `l tgi quist`hl kri tkujgt yhu `l yhur ndkss.  „ Phu oust liim th `milt`by klm kppdy tgi nhrrint sf`dd.  „ Phu eky gkvi th kppdy nhea`lkt`hl hb sf`dds.  „ ^heit`ei yhu eky gkvi th ixtilm tgi nhlnipts

Zgkt th mh ? Kbtir ixke • Qidkx klm sthp whrry`lj kahut ghw yhu pirbhreim. • Mhl‐ Mhl‐tt tg`l tg`lf f thh thh eung eung kah kahut ut tgi tgi s`d s`ddy dy e` e`st stkf kfis is tgkt yhu e`jgt gkvi ekmi.  „ Ivir Iviryh yhli li ek ekfi fi tg tgie ie sh lh li liim im th dh dhhs hsi i yh yhur ur sdiip hvir `t.

• ]kfi arikf bhr nhupdi hb mkys, klm stkrt pripkr`lj bhr lixt yikr ixke. • Qieieair prknt`ni `s tgi fiy, fiy, sh prknt`ni ks eung ks yhu nkl.

]gklf yhu