1. Find all triangle which have integer side lengths with perimeter 36 and integer area.
2. Find a three-digit palindromic number which is 19 times the sum of its digits.
3. Find all four-digit palindromic number which is 352 times the sum of its digits.
4. James has 3 cups of strawberry juice, 3 cups of orange juice and 3 cups of apple juice. he wants to form a straight line arrangement using six of these cups of juice on the table. How many different ways is this possible?
5. Find the last two digits of the number 7^123+9^123+3^123
6. Kimy thinks of two positive integers.He multiplies them together and then subtracts each of the integers from the product, with a result of 35. Find all possible pairs of numbers he could have chosen.
7. Three girls, A, B and C, each have a younger brother, D, E and F, respectively.All six children do some fruit picking for the local farmer.The farmer agrees to pay each child as many dollars per baskets as the number of baskets of fruit collected by that child.Each of the girls earned $45 more than her brother, and all six children collected a different number of baskets.How much did the farmer pay them all in total?