Esercizio 90 giochi matematici scuole superiori – Esercizi svolti – MATEMATICA

Molti numeri di due cifre si possono scrivere come somma di due numeri primi. Quale numero di due cifre ammette il più grande numero di decomposizioni di questo tipo (somma di due numeri primi)?

Esercizio contenuto nella prova della finale italiana del 2016

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Visualizza la soluzione

Numero	Decomposizioni	Numero di decomposizioni
$10$		$0$
$11$		$0$
$12$	$5+7$	$1$
$13$	$11+2$	$1$
$14$	$11+3=7+7$	$2$
$15$	$13+2$	$1$
$16$	$13+3=11+5$	$2$
$17$		$0$
$18$	$13+5=11+7$	$2$
$19$	$17+2$	$1$
$20$	$17+3=13+7$	$2$
$21$	$19+2$	$1$
$22$	$19+3=5+17=13+9=11+11$	$4$
$23$		$0$
$24$	$19+5=17+7=13+11$	$3$
$25$	$23+2$	$1$
$26$	$23+3=19+7=13+13$	$3$
$27$		$0$
$28$	$23+5=17+11$	$2$
$29$		$0$
$30$	$23+7=19+11=17+13$	$3$
$31$	$29+2$	$1$
$32$	$29+3=19+13$	$2$
$33$	$31+2$	$1$
$34$	$31+3=29+5=23+11=17+17$	$4$
$35$		$0$
$36$	$31+5=29+7=23+13=17+19$	$4$
$37$		$0$
$38$	$31+7=19+19$	$2$
$39$	$37+2$	$1$

$40$	$37+3=29+11$	$2$
$42$	$37+5=31+11=29+13=23+19$	$4$
$44$	$41+3=37+7=31+13$	$3$
$46$	$43+3=41+5=29+17=23+23$	$4$
$48$	$43+5=41+7=37+11=31+17=19+29$	$5$
$50$	$47+3=43+7=37+13=31+19$	$4$
$52$	$47+5=41+11=29+23$	$3$
$54$	$47+7=43+11=41+13=37+17=31+23$	$5$
$56$	$53+3=43+13=37+19$	$3$
$58$	$53+5=47+11=41+17=29+29$	$4$
$60$	$53+7=47+13=43+17=41+19=37+23=29+31$	$6$
$62$	$59+3=43+19=31+31$	$3$
$64$	$61+3=59+5=53+11=47+17=41+23$	$5$
$66$	$61+5=59+7=53+13=47+19=43+23=37+29$	$6$
$68$	$61+7=37+31$	$2$
$70$	$67+3=59+11=53+17=47+23=41+29$	$5$
$72$	$67+5=61+11=59+13=53+19=43+29=41+31$	$6$
$74$	$71+3=67+7=61+13=43+31=37+37$	$5$
$76$	$73+3=71+5=59+17=53+23=47+29$	$5$
$78$	$73+5=71+7=67+11=61+17=59+19=47+31=41+37$	$7$
$80$	$73+7=67+13=61+19=43+37$	$4$
$82$	$79+3=71+11=59+23=53+29=41+41$	$5$
$84$	$79+5=73+11=71+13=67+17=61+23=53+31=47+37=43+41$	$8$
$86$	$83+3=79+7=73+13=67+19=43+43$	$5$
$88$	$83+5=71+17=59+29=47+41$	$4$
$90$	$83+7=79+11=73+17=71+19=67+23=61+29=59+31=53+37=43+47$	$9$
$92$	$89+3=79+13=73+19=61+31$	$4$
$94$	$89+5=83+11=71+23=53+41=47+47$	$5$
$96$	$89+7=83+13=79+17=73+23=67+29=59+37=53+43$	$7$
$98$	$79+19=67+31=61+37$	$3$

Brevi lezioni

Esercizio 90 giochi matematici scuole superiori – Esercizi svolti – MATEMATICA

SVOLGIMENTO

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