![]() ![]() ![]() Solution: As only 3 pupils dislike panna cotta, it cannot be the case that 4 or more pupils dislike all three foods. In a class of 30 pupils, 16 like pizza, 19 like pasta and 27 like panna cotta.ġ) What is the largest possible number of pupils who dislike pizza, pasta and panna cotta? Each of the digits 1,2,3 appears equally often in each position, so each appears 9 times in each position. Solution : Among the 27 such three-digit numbers, there are 27 hundreds digits, 27 tens digits and 27 units digits. What is the sum of all three-digit numbers containing the digits 1, 2 and/or 3 (where repeat digits are allowed) but no other digits? Solution: There are 3 choices for each of the 3 digits, so the answer is 3x3x3=27 How many three-digit numbers contain the digits 1, 2 and/or 3 (where repeat digits are allowed) but no other digits ? Hence the smallest possible number of extra games is 15. In this case, it could happen that Haru wins 9 games in total and Karu wins 11. So at least 20 games must be played in total. What is the smallest possible number of extra games that they must play for Karu to have won exactly 55% of all the games? So the mug can hold 50×15/4=187.5ml in total.Īfter 5 games of chess, Haru is beating Karu 4-1. Solution: 50ml represents 3/5-1/3=4/15 of the capacity of the mug. 50ml more tea is poured into the mug, so that it is now 3/5 full. ![]()
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