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9.Roy plays a game with Sam as follows. There are 2 bags, with 1200 and 1800 coinsrespectively. They take away coins from the bags in turns according to the following rules: One may take away coins from only one of the bags each time. At least 1 coin mustbe taken away and one must not take away all the coins in... 顯示更多 9. Roy plays a game with Sam as follows. There are 2 bags, with 1200 and 1800 coins respectively. They take away coins from the bags in turns according to the following rules: One may take away coins from only one of the bags each time. At least 1 coin must be taken away and one must not take away all the coins in the bag. After each round, there must be at least one bag with an even number of coins. Whoever fails to take away coins according to the above rules is the loser while the other player is the winner. If Roy takes away coins first, how many coins should he take away in the first round in order to guarantee that he must win? 11.小明在抽獎裏贏得10 張書店的20 元優惠券（使用細則見下圖）。他打算用 這些優惠券來購買書籤。書籤正價每張3.3 元，但現正推出特價優惠，每張 減收0.8元，而且買九送一，即顧客可以9張書籤的價錢購買10張書籤。若 小明希望得到98張書籤，他最少要付款多少元？ Mike has won ten $20 coupons of a bookstore in a lucky draw. (See the figure below on the terms and conditions.) He plans to buy bookmarks with these coupons. Each bookmark costs $3.3, but a discount of $0.8 per bookmark is now being offered. Furthermore, there is a buy-9-get-1-free promotion which entitles customers to buy 10 bookmarks at the price of 9. If Mike wants to get 98 bookmarks, what is the minimum amount (in dollars) he has to pay? COUPON $20 優惠券 使用細則： Terms and Conditions: 1. 憑券可作20元使用，每次購物限用一張。 This coupon is worth $20. Only one coupon may be used at a time. 2. 以優惠券購物時不能享用特價優惠，但仍可享有買九送一優惠。 No discount will be offered when making purchases with this coupon, but customers can still enjoy the buy-9-get-1-free privilege. 3. 如購物不足20元，餘額不獲發還。 No return will be given for purchases less than $20. 更新: 題解!!!
最佳解答:
9. Always keep the number of coins be 2n and 2n-1, so Roy should take 601 coins from the 2nd bags to make it 1199Subsequently no matter what Sam does, Roy just needs to maintain the ratio 2n,2n-1 For example, Sam makes it 1200, 1197, Roy should make it 1198,1197If Sam makes it 1100,1197, Roy should make it 1100, 1099If Sam makes it 1200, 1020, Roy should make it 1019,1200In this way the number of coins remains 2n and 2n-1 after Roy' s moveUltimately when 2,1 is reached, Sam cannot take further coins according to the rule 11.Pre-calculation:Use 1 coupon to get 6 bookmarks (6×3.3=19.8)=>$0 eachBuy 9 bookmarks without using coupon (9×2.5=22.5) to get 10=>$2.25 eachUse a coupon to buy 9 (9×3.3-20=9.7)=>6 free and 4 at $2.425 eachBuy less than 9 bookmarks without using coupon=>$2.5 eachFirst priority use the coupon 10 times to get 60 bookmarksWe still need 38. Buy 27 to get 30=>$67For the remaining 8, buying separately is not the option as it costs $2.5 eachit is better to combine with the coupons, i.e.2 of the coupons are used to buy 18 bookmarks to get 20Summary:Use a coupon to buy 6 bookmarks for 8 times=>48 bookmarks for freeUse a coupon to buy 9 bookmarks twice=>20 bookmarks at 9.7×2=$19.4Buy 27 bookmarks separetly=>30 bookmarks at 22.5×3=$67.5Total 98 bookmarks at 19.4+67.5=$86.9
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培正數學邀請賽
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發問:9.Roy plays a game with Sam as follows. There are 2 bags, with 1200 and 1800 coinsrespectively. They take away coins from the bags in turns according to the following rules: One may take away coins from only one of the bags each time. At least 1 coin mustbe taken away and one must not take away all the coins in... 顯示更多 9. Roy plays a game with Sam as follows. There are 2 bags, with 1200 and 1800 coins respectively. They take away coins from the bags in turns according to the following rules: One may take away coins from only one of the bags each time. At least 1 coin must be taken away and one must not take away all the coins in the bag. After each round, there must be at least one bag with an even number of coins. Whoever fails to take away coins according to the above rules is the loser while the other player is the winner. If Roy takes away coins first, how many coins should he take away in the first round in order to guarantee that he must win? 11.小明在抽獎裏贏得10 張書店的20 元優惠券（使用細則見下圖）。他打算用 這些優惠券來購買書籤。書籤正價每張3.3 元，但現正推出特價優惠，每張 減收0.8元，而且買九送一，即顧客可以9張書籤的價錢購買10張書籤。若 小明希望得到98張書籤，他最少要付款多少元？ Mike has won ten $20 coupons of a bookstore in a lucky draw. (See the figure below on the terms and conditions.) He plans to buy bookmarks with these coupons. Each bookmark costs $3.3, but a discount of $0.8 per bookmark is now being offered. Furthermore, there is a buy-9-get-1-free promotion which entitles customers to buy 10 bookmarks at the price of 9. If Mike wants to get 98 bookmarks, what is the minimum amount (in dollars) he has to pay? COUPON $20 優惠券 使用細則： Terms and Conditions: 1. 憑券可作20元使用，每次購物限用一張。 This coupon is worth $20. Only one coupon may be used at a time. 2. 以優惠券購物時不能享用特價優惠，但仍可享有買九送一優惠。 No discount will be offered when making purchases with this coupon, but customers can still enjoy the buy-9-get-1-free privilege. 3. 如購物不足20元，餘額不獲發還。 No return will be given for purchases less than $20. 更新: 題解!!!
最佳解答:
9. Always keep the number of coins be 2n and 2n-1, so Roy should take 601 coins from the 2nd bags to make it 1199Subsequently no matter what Sam does, Roy just needs to maintain the ratio 2n,2n-1 For example, Sam makes it 1200, 1197, Roy should make it 1198,1197If Sam makes it 1100,1197, Roy should make it 1100, 1099If Sam makes it 1200, 1020, Roy should make it 1019,1200In this way the number of coins remains 2n and 2n-1 after Roy' s moveUltimately when 2,1 is reached, Sam cannot take further coins according to the rule 11.Pre-calculation:Use 1 coupon to get 6 bookmarks (6×3.3=19.8)=>$0 eachBuy 9 bookmarks without using coupon (9×2.5=22.5) to get 10=>$2.25 eachUse a coupon to buy 9 (9×3.3-20=9.7)=>6 free and 4 at $2.425 eachBuy less than 9 bookmarks without using coupon=>$2.5 eachFirst priority use the coupon 10 times to get 60 bookmarksWe still need 38. Buy 27 to get 30=>$67For the remaining 8, buying separately is not the option as it costs $2.5 eachit is better to combine with the coupons, i.e.2 of the coupons are used to buy 18 bookmarks to get 20Summary:Use a coupon to buy 6 bookmarks for 8 times=>48 bookmarks for freeUse a coupon to buy 9 bookmarks twice=>20 bookmarks at 9.7×2=$19.4Buy 27 bookmarks separetly=>30 bookmarks at 22.5×3=$67.5Total 98 bookmarks at 19.4+67.5=$86.9
其他解答:
請問你是否奧數導師？？？8758B59A7FA1EEA7
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