2022年大联盟(Math League)国际夏季五年级数学挑战活动一(含答案)
《2022年大联盟(Math League)国际夏季五年级数学挑战活动一(含答案)》由会员分享,可在线阅读,更多相关《2022年大联盟(Math League)国际夏季五年级数学挑战活动一(含答案)(12页珍藏版)》请在七七文库上搜索。
1、2022 Math League International Summer Challenge, Grade 5 (Unofficial version, for reference only)Note: There are nine questions in total. Seven questions are worth 10 points each. Two questions are worth 15 points each. The total points are 100.Question 1 (10 Points)Objective:Help as many ladybugs a
2、s possible land on the leaves.Rules:1. Ladybugs arrive in numerical order: Ladybug 1, Ladybug 2, Ladybug 3, etc.2. You help each ladybug choose whether to land on the left leaf or the right leaf.3. If on one leaf, the number of dots on two ladybugs adds up to the number of dots on a third ladybug, a
3、ll of the ladybugs fly away.In the figure below, you put Ladybug 1 on the right leaf. Then you put Ladybug 2, Ladybug 3, and Ladybug 4 on the left leaf. Then you put Ladybug 5 on the right leaf.Now there is nowhere to put Ladybug 6.If Ladybug 6 lands on the left leaf, all of the ladybugs will fly aw
4、ay, because 2 + 4 = 6. If Ladybug 6 lands on the right leaf, all of the ladybugs will fly away, because 1 + 5 = 6.12You saw how to help 5 ladybugs. What is the largest number of ladybugs that you can help in this case? The answer is 8, figure below.Note: You cant skip any ladybugs. For example, the
5、following is not allowed. You place Ladybug 1 and Ladybug 2 on the left leaf. Then you skip Ladybug 3, and place Ladybug 4 on the left or right leaf. This skipping Ladybug 3 is not allowed. Ladybugs arrive in numerical order, and you must place each of them on either leaf in numerical order. This is
6、 true for all the following questions.(a) If only ladybugs that are numbered with powers of 2 (1, 2, 4, 8, 16, 32, 64, 128, ) are out flying, what is the largest number of ladybugs that you can help? Ladybugs still arrive in increasing order.Note: Please enter 0 if your answer is infinitely many, wh
7、ich means you can place as many ladybugs on the leaves as you want. There is no limit.Answer: 0(b) If only ladybugs that are numbered with square numbers (1, 4, 9, 16, 25, 36, 49, 64, ) are out flying, what is the largest number of ladybugs that you can help? Ladybugs still arrive in increasing orde
8、r.Note: Please enter 0 if your answer is infinitely many, which means you can place as many ladybugs on the leaves as you want. There is no limit.Answer: 0(c) If only ladybugs that are numbered with cube numbers (1, 8, 27, 64, 125, 216, ) are out flying, what is the largest number of ladybugs that y
9、ou can help? Ladybugs still arrive in increasing order.Note: Please enter 0 if your answer is infinitely many, which means you can place as many ladybugs on the leaves as you want. There is no limit.Answer: 0(d) If only ladybugs that are numbered with non-multiples of 5 (1, 2, 3, 4, 6, 7, 8, 9, 11,
10、12, 13, 14, 16, 17, 18, 19, ) are out flying, what is the largest number of ladybugs that you can help? Ladybugs still arrive in increasing order.Note: Please enter 0 if your answer is infinitely many, which means you can place as many ladybugs on the leaves as you want. There is no limit.Answer: 0Q
11、uestion 2 (15 Points)Objective:Find the gold bar in as few weighings as possible.Rules:1. You can use a balance scale to compare the weights of two groups of bars.2. Only one bar is gold, and all other bars are counterfeits (fakes).3. The gold bar is a little heavier than each of the counterfeits.4.
12、 All counterfeits weigh the same.5. The appearances of all bars are identical. The only way to find out the gold bar is using a balance scale.Example 1:There are two bars. One is gold. The other is a counterfeit. The gold bar is a little heavier than the counterfeit. You need one weighing to find ou
13、t the gold bar. In the figure below, bar 2 is the gold bar.Example 2:There are four bars. One is gold. The other three are counterfeits. The gold bar is a little heavier than each of the counterfeits. All counterfeits weigh the same. The minimum number of weighings to guarantee to find out the gold
14、bar is 2, figure below. In the figure below, the gold bar is bar 2.Another way to do this is that you first compare two bars. If one is heavier, you are done. Otherwise, you compare the other two bars. Again, the minimum number of weighings to guarantee to find out the gold bar is 2.(a) There are 8
15、bars. One is gold. The other 7 are counterfeits. The gold bar is a little heavier than each of the counterfeits. All counterfeits weigh the same. What is the minimum number of weighings to guarantee to find out the gold bar?Answer: 2(b) There are 9 bars. One is gold. The other 8 are counterfeits. Th
16、e gold bar is a little heavier than each of the counterfeits. All counterfeits weigh the same. What is the minimum number of weighings to guarantee to find out the gold bar?Answer: 2(c) There are 10 bars. One is gold. The other 9 are counterfeits. The gold bar is a little heavier than each of the co
17、unterfeits. All counterfeits weigh the same. What is the minimum number of weighings to guarantee to find out the gold bar?Answer: 3(d) If you can do at most 1 weighing, the largest number of bars you can start with and still find the gold bar is 3. And here is why.Place bar 1 on the left pan, and b
18、ar 2 on the right pan. If bar 2 is heavier, then the gold bar is bar 2, figure below.If the weighing is balanced, figure below, then the gold bar is bar 3.If you can do at most 2 weighings, what is the largest number of bars you can start with and still find the gold bar?Answer: 9(e) If you can do a
19、t most 3 weighings, what is the largest number of bars you can start with and still find the gold bar?Answer: 27(f) Now we have new rules:a. You can use a balance scale to compare the weights of two groups of bars.b. Only one bar is gold, and all other bars are counterfeits (fakes).c. The gold bar i
20、s either lighter or heavier than each of the counterfeits, but you dont know which.d. All counterfeits weigh the same.e. The appearances of all bars are identical. The only way to find out the gold bar is using a balance scale.There are 4 bars. One is gold. The other 3 are counterfeits. The gold bar
21、 is either lighter or heavier than each of the counterfeits, but you dont know which. All counterfeits weigh the same. What is the minimum number of weighings to guarantee to find out the gold bar?Answer: 2(g) There are 8 bars. One is gold. The other 7 are counterfeits. The gold bar is either lighte
22、r or heavier than each of the counterfeits, but you dont know which. All counterfeits weigh the same. What is the minimum number of weighings to guarantee to find out the gold bar?Answer: 3(h) There are 12 bars. One is gold. The other 11 are counterfeits. The gold bar is either lighter or heavier th
23、an each of the counterfeits, but you dont know which. All counterfeits weigh the same. What is the minimum number of weighings to guarantee to find out the gold bar?Answer: 3(i) There are 13 bars. One is gold. The other 12 are counterfeits. The gold bar is either lighter or heavier than each of the
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- 2022年大联盟Math League国际夏季五年级数学挑战活动一含答案 2022 联盟 Math League 国际 夏季 年级 数学 挑战 活动 答案
链接地址:https://www.77wenku.com/p-254389.html