Problem 6 · 2013 Math Kangaroo
Medium
Number Theory
cryptarithmplace-value
In the multiplication below the same digit is used in every box: ?? × ? = 176. Which digit must be used so the calculation is correct?
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Answer: B — 4
Show hints
Hint 1 of 3
Both squares hold the same digit, so the two-digit number is something like 33 or 44.
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Hint 2 of 3
Just try the same digit in every box and see which one multiplies to 176.
Still stuck? Show hint 3 →
Hint 3 of 3
The product ends in 6, so look for a digit whose square ends in 6.
Show solution
Approach: try the same digit in each box
- The same digit goes in all the boxes, so test repeated-digit numbers: \(33\times3 = 99\) (too small), \(55\times5 = 275\) (too big).
- In between, \(44\times4 = 176\), exactly right.
- So the digit is 4, which is choice B.
Another way:
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