HMMT 2002 U61
- Guts
- Answer
Bob Barker went back to school for a PhD in math, and decided to raise the intellectual level of The Price is Right by having contestants guess how many objects exist of a certain type, without going over. The number of points you will get is the percentage of the correct answer, divided by 10 , with no points for going over (i.e. a maximum of 10 points).
Let's see the first object for our contestants...a table of shape (5, 4, 3, 2, 1) is an arrangement of the integers 1 through 15 with five numbers in the top row, four in the next, three in the next, two in the next, and one in the last, such that each row and each column is increasing (from left to right, and top to bottom, respectively). For instance:
1
6
10 11 12
13 14
15
is one table. How many tables are there?
Dataset text NuminaMath olympiads. Quoted with source.
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