# mathcounts problems

**Question description**

80. On a 12-hour digital clock, at how many times during a 24-hour day will all of the digits showing the time be the same?

77. The surface area of a sphere, in square meters, and its volume, in cubic meters, are numerically equal. What is the length of the radius of the sphere?

78. Ben won a writing contest at school. To determine his prize, he draws slips of paper from a bag containing 16 slips, with the names of 4 different prizes written on 4 slips each. He continues to draw slips without replacement until he has selected 4 slips for the same prize. What is the maximum number of slips that Ben can draw without knowing his prize?

74. Given that the Earth is turning at a constant rate around its axis and it makes exactly one complete rotation every 24 hours, how many degrees does the center of home plate at Fenway Park rotate around Earth’s axis from 6 a.m. on May 8th to noon on May 10th of the same year?

76. What positive four-digit integer has its thousands and hundreds digits add up to the tens digit, its hundreds and tens digits add up to its ones digit and its tens and ones digits add up to the two-digit number formed by the thousands and hundreds digits?

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