1
Calculate the product of all the numerical digits displayed on a standard telephone dial.
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Solution: Step 1: Identify all the numbers present on a standard telephone dial. These numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
Step 2: Understand the property of multiplication: any number multiplied by zero results in zero.
Step 3: Since the set of numbers on the dial includes '0', when all these numbers are multiplied together, the presence of '0' will make the entire product zero.
Product = 0 * 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 = 0.
12
A bird shooter was asked about the number of birds in his bag. He responded: 'All are sparrows except six, all are pigeons except six, and all are ducks except six.' How many birds were in his bag in total?
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Solution: Step 1: Let 'S' be the number of sparrows, 'P' be the number of pigeons, and 'D' be the number of ducks.
Step 2: Let 'Total' be the total number of birds in the bag. So, Total = S + P + D.
Step 3: "All sparrows but six" means that the non-sparrow birds (pigeons + ducks) sum to 6. Thus, P + D = 6 (Equation 1).
Step 4: "All pigeons but six" means that the non-pigeon birds (sparrows + ducks) sum to 6. Thus, S + D = 6 (Equation 2).
Step 5: "All ducks but six" means that the non-duck birds (sparrows + pigeons) sum to 6. Thus, S + P = 6 (Equation 3).
Step 6: We have a system of three linear equations:
1. P + D = 6
2. S + D = 6
3. S + P = 6
Step 7: From Equation 1 and Equation 2, since P + D = 6 and S + D = 6, it implies that P must be equal to S.
Step 8: Substitute P = S into Equation 3: S + S = 6 => 2S = 6 => S = 3.
Step 9: Since S = P, then P = 3.
Step 10: Substitute P = 3 into Equation 1: 3 + D = 6 => D = 3.
Step 11: So, there are 3 sparrows, 3 pigeons, and 3 ducks.
Step 12: The total number of birds in the bag = S + P + D = 3 + 3 + 3 = 9.
14
Five siblings are assigned to different houses (Blue, Black, Yellow, White, Green) and sports teams (Chess, Football, Tennis, Rugby, Shotput). Given certain constraints, which house is assigned to the sibling who plays Rugby?
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Solution: Step 1: Process given information
1. A (Chess) not in Black house
2. C in White house
3. Tennis in Green house
4. D, B not in Rugby
5. B in Blue house
6. E in Shotput
Step 2: Deduce house for Rugby
From constraints: C in Rugby and White house
Step 3: Conclusion: White house