If the digits 7, 8, 2, 3 and 0 are used, each exactly once, to form a three-digit positive integer and a two-digit positive integer that differ by exactly 288, what is the sum of the three-digit integer and the two-digit integer? (Difficulty: 4)
數(shù)字7、8、2、3、0各使用一次，組成一個(gè)3位自然數(shù)和一個(gè)2位自然數(shù)，使得它們正好相差288，求這個(gè)3位數(shù)和2位數(shù)的和是幾？
先列一個(gè)豎式：
圖1
差的個(gè)位是8，在數(shù)字7、8、2、3、0中，只有 0和2 滿足條件，填入得：
圖2
差的十位是8，因?yàn)閭�(gè)位借了1，在剩下的7、8、3中，只有 7和8 滿足條件，填入得：
圖3
剩下最后一個(gè)方框中只能填3了，檢查一下符合條件！
圖4
故它們的和為452：
圖5
下期看點(diǎn)——難倒美國(guó)小朋友的數(shù)陣圖
Positive integers 1 to 36 are written in rows in a six-by-six array as shown. Each prime number is crossed off, as well as all the numbers in the diagonal extending up and to the right from that prime. For example, 11 is prime and is crossed off along with the 6 above and to the right. What is the sum of the remaining values after all the primes and associated diagonals have been eliminated? (Difficulty: 3)
圖6
