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Solution |
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3) Damian has a 7 digit phone number. The first 3 digits are consecutive in strictly decreasing order and sum to 6. The last 4 digits is a number that is the product of the squares of two consecutive numbers and it is as large as possible. What is Damian's phone number?
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1. There are only 3 numbers in decending order that sum to 6.
These 3 numbers are 3, 2, and 1
2. Fill out this table until you find 2 numbers that are consecutive and their squares multiply to under 9999:
| N | N1 =
N+1 | N2 | N12
| N2 x N12 |
| 8 | 9 | 64 | 81 | 5184 |
| 9 | 10 | 81 | 100 | 8100 |
| 10 | 11 | 100 | 121 | 12100 |
3. Put the first 3 numbers together with these 4 numbers (the last column) to
make the telephone number: 321-8100
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4) It's Joni's lucky day and she finds $2.88 in coins while walking across a parking lot. She decides
to share a little of it with her two friends. They each get 1/8 of the amount and she keeps the rest. What is the fewest number of coins she could give one of her friends and what are they?
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1. Convert the sum to cents = 288
2. Divide this by 8 to get what each friend gets = 36 cents.
3. Figure out the fewest coins, starting with quarters =
1 quarter, 1 dime and 1 penny = 3 coins
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5) Using the operations addition, subtraction, multiplication, or division in any order you need to
how can you get the number 1 using exactly five 2s? Insert the operations you need and parentheses to make the equation true or tell us what you did.
2 __ 2 __ 2 __ 2 __ 2 = 1
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Work backwards.
1. Assume the last operator is a minus, making the last operation - 2.
2. Then, is there a way with the first 3 operators and the first 4 2s (and some parentheses) to make a 3?
3. The operations are:
(2 + 2 + 2) / 2 - 2 = 6/2 - 2 = 3 - 2 = 1
Note: There are other possibilities, but this is the simplest one.
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