Guaranteed To Make You Think!!

Put on your thinking cap and see how many of the following you can solve!!

1. Use the numbers 20, 10, -4, -2, and -1, and the signs +, -, x, and / to obtain the HIGHEST and the LOWEST numbers possible. All numbers and operations MUST be used once for each problem, and the answers MUST be integers!
2. Find four consecutive ODD integers whose sum is -80 (you must show me your equation too).
3. A standard deck of cards contains 52 cards - four groups (2 black suits and 2 red suits) of 13 cards. Each suit contains an ace, king, queen, jack, and the numbers 10 thorugh 2. Assuming the deck has been shuffled - find the porbability of drawing the following cards (express your answer in simplest form)
• A red card
• A king
• A queen or a jack
• An even number
• The 7 of hearts
• A prime number
4. Palindromes are numbers, words, phrases, or sentences that are read the same from left to right as from right to left. For example: (words) RADAR, BOB, DAD, (phrase) A MAN A PLAN A CANAL PANAMA, (sentence) MADAM I'M ADAM, (numbers) 22, 303, 1991.
• Find two palindromes whose sum is a palindrome.
• Find two palindromes whose difference is a palindrome.
• Do you think it is always true that if the sum of two palindromes is a palindrome, their difference is also a palindrome? Explain!
• Create a phrase or sentence that is a palindrome.
5. Secret codes & ciphers - a cipher is a secert system of writing in which every letter is replaced by a symbol. Can you decipher the following cipher???
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Which problem was most challenging for you? Why? What strategy did you use to meet the challenge??