Unit 16
Akal Pintar
Pak Samad mengisi sebuah bakul dengan 45 biji buah: a biji mangga dan b biji jambu.
Bilangan mangga ganjil. Bilangan jambu genap.
Berapakah mangga dan jambu yang mungkin ada?

奇数加偶数 = ganjil tambah genap
篮子里有 45 个水果,芒果 a 个、番石榴 b 个,而且 a 要是奇数、b 要是偶数。答案不止一组,我们要学会有系统地找出几组可能的值,并检查每一组是否符合条件。
例子:a = 5、b = 40,5 是奇数、40 是偶数,5 + 40 = 45,符合。
注意:两个条件和总数都要同时满足。
odd plus even = ganjil tambah genap
A basket holds 45 fruits: a mangoes and b guavas, where a must be odd and b must be even. There is more than one answer, so we learn to find several possible pairs in an orderly way and check each one.
Example: a = 5 and b = 40: 5 is odd, 40 is even and 5 + 40 = 45, so it works.
Watch out: every pair must meet both conditions and give the right total.
Petua
Genap dan ganjil apabila ditambah
ganjil + genap = ganjil
ganjil + genap = ganjil (3 + 4 = 7)
genap + genap = genap (2 + 6 = 8)
ganjil + ganjil = genap (5 + 1 = 6)
奇偶相加的规律 = corak tambah genap dan ganjil
奇数加偶数一定是奇数;偶数加偶数是偶数;奇数加奇数也是偶数。45 是奇数,正好可以由一个奇数加一个偶数得到,所以这道题有答案。
例子:11 + 20 = 31(奇 + 偶 = 奇);13 + 15 = 28(奇 + 奇 = 偶)。
注意:如果总数是偶数,就不可能是一奇一偶。
odd and even sums = corak tambah genap dan ganjil
Odd + even is always odd; even + even is even; odd + odd is also even. 45 is odd, so it can be made from one odd number and one even number, and the puzzle has answers.
Example: 11 + 20 = 31 (odd + even = odd); 13 + 15 = 28 (odd + odd = even).
Watch out: if the total were even, it could not be one odd and one even number.
Cara bersistem
Pilih a ganjil, kemudian cari b
b = 45 − a
| a (ganjil) | 1 | 3 | 5 | 7 | … | 43 |
|---|---|---|---|---|---|---|
| b = 45 − a | 44 | 42 | 40 | 38 | … | 2 |
有系统地列出 = senaraikan secara bersistem
先让 a 取最小的奇数 1,再依次取 3、5、7……,每次用 b = 45 − a 求出 b。这样一行一行列成表,就不会漏掉或重复。可以看到每个 b 都是偶数。
例子:a = 21 时,b = 45 − 21 = 24。
注意:如果两种水果都至少有一个,a 最大是 43;0 也是偶数,若允许没有番石榴(b = 0),a 也可以是 45。
list in an orderly way = senaraikan secara bersistem
Start with the smallest odd number, a = 1, then take 3, 5, 7 and so on, each time working out b = 45 − a. A table keeps the pairs in order so none are missed or repeated. Every b turns out to be even.
Example: when a = 21, b = 45 − 21 = 24.
Watch out: if there is at least one of each fruit, a goes up to 43; since 0 is even, a could be 45 if b = 0 were allowed.
Semak
Pasangan manakah mengikut semua syarat?
逐项检查 = semak setiap syarat
题目要找出同时符合全部条件的一组 a 和 b。每一组都要检查三件事:a 是不是奇数(看个位);b 是不是偶数(看个位);a + b 是不是刚好等于 45。三项都对才算符合,有一项不对就划掉。
例子:a = 9、b = 36:9 是奇数,36 是偶数,9 + 36 = 45,三项都符合。
注意:有的组奇偶对了但总数不对,有的组总数对了但奇偶放反了,三个条件缺一不可。
check each condition = semak setiap syarat
Find the pair that meets every condition. For each pair check three things: is a odd (look at its ones digit), is b even, and do they add up to exactly 45? Cross out any pair that fails one check.
Example: a = 9 and b = 36: 9 is odd, 36 is even and 9 + 36 = 45, so all three checks pass.
Watch out: some pairs have the right odd and even numbers but the wrong total, and some have the right total with odd and even swapped.
Ringkasan
Syabas!
ganjil + genap = ganjil
Pilih a ganjil, kemudian cari b dengan menolak. Semak semua syarat.
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