GRADE 7-8 / Age 12-14The Three Challenges
1. Mr. Baffle seemed to be quite taken with the brilliant student, who was a guest of Professor Smarty. He wanted to ask her age, but not wishing to appear rude, he asked her instead to reverse the digits in her age and add the resulting number to her age. He then asked her to tell him the largest number less than 11 by which the final result was divisible. The student replied that this number was 10. Baffle, knowing that she must be younger than 28, then knew her age at once. What was it?
2. Using only the numbers on a telephone dial and as many addition and multiplication signs as you like, make the number 100 using each digit once and once only?
3. Talking about the numbers on a telephone dial, which of the digits 0 to 9 appears least and which appears most in the number from 1 to 100?